By "our culture," do you mean the US? Or White Anglo-Saxon Protestants? Or do you have some other understanding of "our culture"?
One of the problems is the word "marriage" means something very different to different people. To a Christian, it may have the above meaning, but let's face it, an atheist really doesn't care what God thinks, and has made no "decision before God." I understand if you think that means an atheist isn't "really" married, but in the US, atheists have the right to marry, so we need to think of a different definition of the word "marriage" when discussing something that applies to people who may not be Christian.
Personally, I think the word "marriage" should be eliminated completely, because I don't see any way for us (Christians and non-) to agree about what it is. I think the US should not grant rights based on marital status, but on "civil unions." Any couple who wants to receive the legal rights this country offers should need to get a "civil union," and such couples can be any consenting adults. And if a couple wants to make a decision before God, and celebrate that decision, it can be done in a Church, called "holy matrimony," and such a rite has absolutely no secular legal benefits. (The religious benefits of a godly marriage cannot be disputed! I'm talking about inheritance rights, joint property, etc.) Most of us Christians would get both, but they would be separate affairs offering completely different things.