In light of the recent resignations of two North Carolina magistrates, explained by their religious convictions that same-sex marriage is a sin or desecrates the "holy institution established by God Himself," I would like to offer a few points of clarification to the overall discourse.
First, the kinds of relationships that qualify for marriage in the Bible, and thus could count as "biblical marriage," represent quite a striking range of options. They include polygyny (more than one wife or concubine, simultaneously), open marriage for the man (since he can have access to the female slaves or servants in the house), forcing a woman to marry her rapist (Deuteronomy 22:28-29) and levirate marriage (wherein a childless widow must marry the brother of her deceased husband). Those are just a few of the examples from the Hebrew Bible.
What we see in the Newer Testament includes Jesus claiming that men can leave their wives and children in order to follow him (Luke 18:28-30), in addition to him somewhat throwing the gauntlet in Matthew 19:10-12, where he discusses men being made eunuchs or making themselves such for the sake of the kingdom: "Let anyone accept this who can." Paul, the man who got the Christian movement started, says in 1 Corinthians 7 that he wished that everyone was as he was, which he clarifies later as being celibate. In the same chapter, Paul's letter endorses equality between husband and wife in a marriage. This idea is later countered in Ephesians 5 when the writer endorses a return to the patriarchal ideal of men ruling over their wives. I think most people are simply unaware of the range of possibilities that qualify, regardless of which testament of the Bible we look to.
The second point I would like to clarify is that, aside from that one moment in 1 Corinthians 7, marriage is discussed in terms of the woman as the property of the man. I say this with a fairly literal sense intended. It does explain why or how so many biblical stories show wives being treated as less than fully human, but I do hope that people who love the Bible can admit that this is an element of it that we ought not to continue to endorse.
Third, when people say that the "Bible says homosexuality/gay marriage is a sin," I know that they believe that the Bible says this, since I used to think so, too. But it does not. There are passages such as the Sodom story (Genesis 19), which depicts every male in the town gathering to gang rape some visitors. The issue there is not "gay sex," but rather that these men were just plain cruel to outsiders. The scene would have been no less offensive if Lot had succeeded in giving the men his two virgin daughters to do to them as they pleased. That is about cruelty. There are other passages people turn to, such as Leviticus 18:22, and focus on men having sex as an abomination. But they do not take into account why. Just as in Genesis 38, where Onan is struck dead for avoiding getting his sister-in-law pregnant by pulling out early, the issue is about the people of Israel needing to grow in numbers. Any wasting of semen was not to be tolerated and thus was an abomination. None of those situations are talking about two same-sex people in loving relationships.
Finally, there is no specific place where "God Himself" establishes marriage as a holy institution. Genesis 2:24 is talking about the fact that humans do have an urge to leave home and start their own families. The "and cling to his wife" phrase can (and perhaps ought to) be translated as "cling to his woman." We read into this passage the idea of marriage, mainly due to the translations we are reading. One can read Ephesians 5:21-33, where marriages are discussed as representing the head/body hierarchy of Christ to the Church, as God making marriage holy. But that is certainly not how it was established, and one might challenge the level of submission that is required of the wives in that situation as being something other than holy.
When I hear someone say she only believes in "biblical marriage," my knee-jerk reaction is to want to ask her which version she is referring to. I also find myself wanting to remind her that love is never discussed as foundational to marriage. Thus, while same-sex marriage is not endorsed in the Bible, neither is a loving, mutually agreed upon union of a man and woman.