Does the Bible contain a definitive explanation of morality? Or does it leave room for interpretation on the matter of what is moral and what is immoral? Perhaps it depends on the tradition?
All language, whether written or spoken, whether miraculously inscribed on stone tablets, breathed in fire letters on the sky, inspired by God through a human vessel or scribbled to your friend on Facebook—due to the fundamental nature of language as a means of communication—requires interpretation. Interpretation is an inseparable part of communication.
Most branches of Christianity (as in the vast majority) believe God has provided in the Bible a clear basis—fundamental guidelines as you will—for morality. It defines what makes something moral vs. immoral and provides concrete examples.
The doctrine in question here that I assume is what you actually mean to question is officially known as the Perspicuity of Scripture. The degree to which different doctrinal traditions believe the Scripture to be clear (as in plain to the ordinary reader) varies some with some traditions believing it to need more contextualization. However on the issue of basic morality the weight of extant teachings is clearly towards the end of believing it to be spelled out clearly.
You will find this issue covered specifically in the statement of faith of most groups.
What follows is one example of that. While the Westminster Confession of Faith as a whole is only officially representative of a limited subset of Protestants, you will find at least on these two points it is generally representative of many groups. At the very least this point (whether doctrinally the same or different) turns up in similar statements for most groups.
For example on the general nature of Scripture being clear (not needing scholarly interpretation beyond the ordinary understanding of language) it has this to say:
WCF, Chapter 1
VI. The whole counsel of God concerning all things necessary for His own glory, man's salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture […]
VII. All things in Scripture are not alike plain in themselves, nor alike clear unto all: yet those things which are necessary to be known, believed, and observed for salvation are so clearly propounded, and opened in some place of Scripture or other, that not only the learned, but the unlearned, in a due use of the ordinary means, may attain unto a sufficient understanding of them.
On the issue of morality, it notes that the fundamental rules governing morality are outlined in the Ten commandments (this idea is expressed in various ways but generally held across most theological traditions).
(Emphasis mine to note the thread relevant to this question in a longer excerpt.)
WCF, Chapter 19
I. God gave to Adam a law, as a covenant of works, by which He bound him and all his posterity, to personal, entire, exact, and perpetual obedience, promised life upon the fulfilling, and threatened death upon the breach of it, and endued him with power and ability to keep it.
II. This law, after his fall, continued to be a perfect rule of righteousness; and, as such, was delivered by God upon Mount Sinai, in ten commandments, and written in two tables: the first four commandments containing our duty towards God; and the other six, our duty to man.
III. Besides this law, commonly called moral, God was pleased to give to the people of Israel, as a church under age, ceremonial laws, […]
V. The moral law does forever bind all, as well justified persons as others, to the obedience thereof; and that, not only in regard of the matter contained in it, but also in respect of the authority of God the Creator, who gave it. Neither does Christ, in the Gospel, any way dissolve, but much strengthen this obligation.
VI. Although true believers be not under the law, as a covenant of works, to be thereby justified, or condemned; yet is it of great use to them, as well as to others; in that, as a rule of life informing them of the will of God, and their duty, it directs and binds them to walk accordingly; discovering also the sinful pollutions of their nature, hearts and lives; so as, examining themselves thereby, they may come to further conviction of, humiliation for, and hatred against sin, together with a clearer sight of the need they have of Christ, and the perfection of His obedience. It is likewise of use to the regenerate, to restrain their corruptions, in that it forbids sin: and the threatenings of it serve to show what even their sins deserve; and what afflictions, in this life, they may expect for them, although freed from the curse thereof threatened in the law. The promises of it, in like manner, show them God's approbation of obedience, and what blessings they may expect upon the performance thereof: although not as due to them by the law as a covenant of works. So as, a man's doing good, and refraining from evil, because the law encourages to the one and deters from the other, is no evidence of his being under the law: and not under grace.
From the fifth law to the tenth, The Ten Commandments gave us moral laws such as disrespecting parents, murder, adultery, stealing, lying and coveting. There are many other moral laws given in the Old Testament such as, lending money to others without profit, showing mercy to the poor etc.
However, Jesus made it much simpler to understand by summing up the whole Old Testament Laws into only TWO.
Matthew 22:35-40 (NIV)
One of them, an expert in the law, tested him with this question: “Teacher, which is the greatest commandment in the Law?” Jesus replied: “‘Love the Lord your God with all your heart and with all your soul and with all your mind.’ This is the first and greatest commandment. And the second is like it: ‘Love your neighbor as yourself.’ All the Law and the Prophets hang on these two commandments.”
"Love your neighbor as yourself". This truly sums up all the moral laws in a single statement. If you love someone, you will never do anything to harm him/her. There are many ways to harm a person. At the worst, you can kill him and at the least, you can say negative things about that person to others. By cheating your wife, you are hurting her. By stealing from others, you create problem for others. By telling lies, you create injustice. By lending money with interest to those who need it, you are robing them. There can be many examples.
We all have the knowledge of Good and Evil: Because Adam and Eve ate the fruit from the tree of the knowledge of good and evil (Genesis 2:17), the law is in our hearts. We can decide what is morally right and what is not. However, we are inclined to follow the evil side because sin is inherent in us.
Romans 2:14-15 (NIV) Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.
The Bible does not provide a moral theory, rather it provides the doctrine of grace for salvation, such that no person can save themselves through some moral theories or codes.
God commands us to do unto the other as you would have done unto yourself. This is not morally consistent. A moralist here seeks to comply because they wish to be moral before God and brethren. However, by taking the commandment to be a moral code, they equally deem those not complying as immoral. This however is a charge that they would not have done to them, thus, they become hypocrites and immoral through the false assumption that the command is a moral code.
Only those elected by God can keep this command, because Jesus fulfils that command within the us through grace ("I have come to fulfil the law", "Thou in me and I in them"), such that there is nothing about the person in keeping the command, moral, immoral or otherwise. Jesus fulfils the law in us.
We all agree that the Bible contains an explanation of morality, but the question is whether it contains a definitive explanation of morality: one that is complete, accurate, and considered to be the best of its kind; not able to be argued about or changed; final and settled. Or, in the words of the question, does it leave room for interpretation?
It is accepted wisdom that as long as one is guided by the Ten Commandments and the Golden Rule, then one will always adhere to the highest standards of morality. If in practice that is not the case then the Bible, although helpful, is not definitive.
The Ten Commandments
The Ten Commandments are held in the highest esteem by Christians as a guide to live by, but I believe this reflects the awe in which they are held because they were given to Moses by God, as explained in Exodus 31:18,34:4-29, and not because we turn to the Commandments whenever deciding on a course of action. In large part, they are not really about moral behaviour. The first three commandments require believers to worship God only which, important as they are, are not moral instructions. Similarly, the fourth commandment is about religious observance - keeping the Sabbath. Then the fifth commandment tells us to honour our parents, which is a commandment more about family relations than ethics. The next four commandments are concerned with moral values: prohibiting murder, adultery, theft and false witness. The tenth commandment is only concerned with what we think, and is once again about protecting property rights.
Given some thought, the Ten Commandments are not definitive. For example, the seventh commandment prohibits adultery and the tenth prohibits coveting a neighbour's wife. Adultery was more narrowly defined in the Bible than it is today, and was concerned with protecting the property rights of husbands only. We can not clearly define this as dealing with pre-marital sex, even though the seventh commandment is often quoted for this purpose, nor is there a commandment against rape, under-age sex or other similar moral wrongs. The commandment against theft seems straight-forward enough, but does it cover fraud, tax evasion or tax avoidance? The tenth commandment's injunction not to covet a neighbour's slaves (usually translated into English as "manservants and maidservants") is not a moral guide by modern standards.
The Golden Rule
The Golden Rule taught by Jesus (Matthew 7:12, Luke 6:31) is the most famous and, for all its simplicity, most comprehensive moral rule ever spoken. But it is not definitive in that we can refer to it whenever deciding whether something is right or wrong.
Should a definitive explanation of morality deal with complex situations where we must make a choice between two imperfect alternatives? In the Church Father Augustine's unqualified absolutism, lying to ward off rape, or even to save a life, is strictly forbidden, for a person's choice is really between the permission of another's sin or the commission of his own sin. In Augustine's understanding, lying is never justified, yet Norman L. Geisler says in Christian Ethics, page 81, that on the face of it the Bible seems to record many cases of justified lying. Then Augustine dissembles when faced with a quite contrary biblical example, arguing that Jacob's alleged deception of his father, Isaac, in order to obtain blessing, was not a lie but only a “mystery”. So Augustine, one of early Christianity's greatest thinkers, tied himself in knots because there was no definitive explanation of morality that he could turn to.