Or does the bible 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:
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.)
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.
"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.