I'm the same way, it's a terrible situation, but being with an unbeliever was without a doubt the hardest and most heart-wrenching experience of my life. As far as introducing her to Christ, she only became resentful of Christianity because she saw that it was keeping us apart. It's a game of a tug-of-war, both sides trying to pull the other person over. Most of my life I thought that if I wanted something enough I could have it; God taught me that I couldn't, that there were things that were never meant to be mine. I don't have the power to save people, only God does. But in the moment, it felt like it was only a day away; that one day I would wake up and find that she was saved. It's like holding your breathe underwater hoping that someone will drain the ocean.
So that's my experience, but that doesn't even touch the problems that would come later. I'm not one to care if something is not done or not accepted if I don't find that it is morally wrong, and likewise I am not one to do something just because everyone does it. But supposing that I married the unbeliever I still had a terrible problem, the kids. I've heard people say things like, "I'd let the children decide", but I knew this was nonsense. I suppose these parents would let their children decide whether or not to learn math, or history, afterall, "you can't force your beliefs on your children". Maybe the kids will grow up to not believe in traditional mathematics, or they'll believe that Abraham Lincoln didn't exist, but that doesn't mean that I'm not going to teach them what I believe to be true. Not teaching your children about something so important is like not speaking English around them so that they might choose their own language once they are all grown up.
Supposing that the spouse is okay with my teaching the kids about Christ, and Christian morality, there is still a problem. My father and mother both provide very different incites into Christianity. Seeing where they are different and where they are the same has kept me from seeing Christianity as a "one-trick pony". Sometimes I cannot relate to the way my mother talks about Jesus, but my father can say something that makes leaves me enlightened. Sometimes my mother provides some practical way to love someone that my father wouldn't talk much about. As a child, if my mother was the only Christian, what Christian male would I have to look up to? Afterall, if my father wasn't going to church, it couldn't be all that important. And in the end, how would I feel on their deathbed, knowing that they were going to hell?
This is all supposing the "best case" scenario though. More likely, the differences in morality, belief about facts, and daily practices will amount to terrible disagreements. I have heard of too many women that married unbelievers and found they were addicted to pornography, or alcohol, or some other vice, often ending in divorce.
Because I find that I am often attracted to nonbelievers, I figured there are two explanations: Either my relationship with God is not strong enough (this was definitely true when I dated the nonbeliever), or God wants me to be alone (at least right now). I am currently working under the assumption that it is both. If, after strengthening my relationship with God, he wants me to be with a Christian girl then He will give me the affections, and if not, that's fine as well.
Naked I came from my mother's womb, and naked I will depart. The LORD gave and the LORD has taken away; may the name of the LORD be praised. - Job 1:21
