Many interpretations argue that the Song of Solomon is about both the relationship between husband and wife and about Christ and his Church. This stems in large part from Paul's words to the Ephesians:
Wives, submit to your own husbands, as to the Lord. For the husband is the head of the wife even as Christ is the head of the church, his body, and is himself its Savior. Now as the church submits to Christ, so also wives should submit in everything to their husbands.
Husbands, love your wives, as Christ loved the church and gave himself up for her, that he might sanctify her, having cleansed her by the washing of water with the word, so that he might present the church to himself in splendor, without spot or wrinkle or any such thing, that she might be holy and without blemish.
In the same way husbands should love their wives as their own bodies. He who loves his wife loves himself. For no one ever hated his own flesh, but nourishes and cherishes it, just as Christ does the church, because we are members of his body.
“Therefore a man shall leave his father and mother and hold fast to his wife, and the two shall become one flesh.”
This mystery is profound, and I am saying that it refers to Christ and the church.
Paul quotes from Genesis 2 in his letter, referring to God creating woman from man in order to be one with each other:
So the LORD God caused a deep sleep to fall upon the man, and while he slept took one of his ribs and closed up its place with flesh. And the rib that the LORD God had taken from the man he made into a woman and brought her to the man.
Then the man said,
“This at last is bone of my bones
and flesh of my flesh;
she shall be called Woman,
because she was taken out of Man.”
Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh. And the man and his wife were both naked and were not ashamed.
Paul's point is that husband and wife were created to be one body, just as Christ and his Church are one body, and the Church exists because of Christ. With that in mind, you can see why Song of Solomon has been interpreted by the Church as referring to the relationship between Christ and his Church.
Even in the Old Testament, the relationship between God and His people was often compared to the marital relationship. In the book of Hosea, for instance, God has Hosea take a prostitute as a wife to demonstrate to the people of Israel how they have committed adultery against the Lord (cf. Hosea 1:2).
Then, in the New Testament this is seen most fully in Revelation at the marriage of the bride (the Church) and the groom (Christ) where they are united in perfect communion for eternity. See, for example, Revelation 19:7 and 22:2ff.
So, taken together, the marital relationship is good; it's God-ordained and provides us with an image of His relationship to His people. Thus, Song of Solomon can be seen as both a love song between husband and wife and between Christ and his Church.