Bible scholars used to think that the Song of Songs/Solomon was some sort of theological treatise concerning Christ and the church. John Gill was one of those scholars, and his commentary on the Song would make you think you are reading a different book entirely. A statement like, "I adjure you, O daughters of Jerusalem, by the gazelles or the does of the field, that you not stir up or awaken love until it pleases" (Song of Solomon 3:5), he takes to mean is an instruction for believers not to make Christ angry with their bickering and lack of unity in the church. As much as I personally respect John Gill (and others who share this view), I think that he's missed the easy point here. This is a love poem, even if it is about Christ and the church, and the instruction to "not rush the love" is one that we naturally understand in that context.
On the other hand, it has become rather vogue in today's Christian climate to think that the Song of Songs is really just a love song between human lovers that pictures the rapturous joy of human sexuality, and that the only lessons that we can learn about Christ and the church from it are learned by proxy as we think of Ephesians 5. In other words, we know that this man in the Song is totally wrapped up in his wife (and she in him), and we know that in Ephesians 5 husbands are told to love their wives like Christ loved the church; and so we conclude that if Christ's love for the church is anything like what we see in the Song, then He is really wrapped up in His church and she ought also to be wrapped up in Him.
Well, just as much as the first view seemed really complicated, this view seems overly simple, and other respectable Bible scholars have gone too far down this path and turned the Song of Songs into a sex manual for human couples.
I don't think we ought to separate the two. There is much here that makes us think of human sexuality. The man saying that his wife's breasts are like the fruit on a tree and that he is going to climb the tree and grab the fruit (Song of Solomon 7:7-8) is unmistakeably sexual, but at the same time it is also a statement of Christ's pleasure with the fruitfulness of His New Covenant bride. He was very angry with the Old Covenant people of Israel for being a barren tree (remember the time he cursed the fig tree?). He even told the religious leaders that He was going to remove the Kingdom from Israel and give it to a people producing its fruits (Matthew 21:43).
Ultimately, it seems that the problem most of us suffer from (and I definitely include myself in this category) is that we don't really know what to do with poetry. It's deep and there are layers of meaning, but there are not very many solid parts. It's kind of slippery - it resists being formed into structures. It is meant to give us impressions and feelings, not precise instructions. And yet, a good deal of the Bible is written in poetic form. We need to train ourselves better on how to see what we're meant to see and feel what we're meant to feel as we read books like the Song of Solomon, or the Psalms, or the prophets. If we think too analytically about them, we're going to fall off one side of the slope, and if we simplify them too much, we'll fall off the other.