Thanks so much to everyone who responded. I really appreciate the level of responses I have gotten and Im happy to see that there are many examples of relationships like this working!
My general problem is that I could possibly forsee scenarios in the future in which her belief causes a rift in our relationship. I guess its a risk to take if I want to continue with her.
A lot christians to me are Bible cherry-pickers. They pick and choose what parts of the Bible they want to listen to. There are plenty of passages telling you not to date or associate with non-believers. So then why does she ignore the Bible?
One of the things I dislike about religion is the divisiveness. I've seen people reject one another in the past solely on the basis of religious belief and thought to myself "hah, how ridiculous - breaking up over non-existant deities." If I broke up with her for a reason like that it would make me a hypocrite, I think. Therefore, Im gonna try to make it work and see where it leads down the road.