I am a vegetarian, and my husband is not. He knew when we met that I was a vegetarian, just like I knew that he was not one. While he eats slightly fewer animals, than he used to, he still has no desire to become a vegetarian.
Like you, I don't cook meat - I don't even know how; I'd probably end up giving someone food poisoning. I don't want any of my money going to pay for it. I don't want to clean up after it. I don't want it in my fridge, and I definitely don't want my kids eating it. So what's a girl to do?
My husband and I just don't eat the same things, or when we do eat the same thing, he makes the meat and adds it at the last minute. We both love pasta, so we'll make pasta, and he'll make meat sauce for himself and I'll have plain tomato sauce ... or something along those lines. It seems really difficult at first, but it's actually not that hard. We can make pizza together, and he can add pepperoni to his half. Or if we're making tacos, I can use the "fake" meat and he can make the real thing. Then he cleans his dishes, and I clean mine. It's at least one way to make sure we're each responsible for cleaning up after ourselves.
I don't purchase the meat. If he wants it, he has to make a special trip to the store to get it. Usually he forgoes the meat because he doesn't want to go to the trouble of getting it, cooking it, and cleaning up after it. But if he wants it, he knows the rules about it. As for storing it in the fridge, since it is his house, too, there's not a lot I feel I can say about that. We do keep a separate bin in there, though, for the meat storage. That way I don't have to look at it or worry about it contaminating any other food.
He has come around to drinking soy milk instead of real milk. I'm hoping that some day he'll decide to go vegetarian, but if he doesn't, it will work out for us.
Children might make things more complicated. I definitely want to raise vegetarian kids, at least until they are old enough to make an informed decision for themselves. That brings up the question, "Well, when are they old enough? When they're old enough to ask for meat or when?" I was 10 when I became a vegetarian. I don't necessarily think that there is a specific age that will determine when a child is ready ... I think it depends on each child and their maturity. My husband and I discussed it, and decided that when our kids come to us and ask why I eat meat and my husband doesn't, and then are able to comprehend our answers and explanations, that will be the time for them to decide what they want to eat.
Until that point, they will be vegetarian. We discussed this, and decided that since I am the one who will do most of the child rearing and cooking/feeding of our children, that it will be my decision to make. Of course, I know that there will be times when he'll be alone with the kids and McDonald's will seem like an easy and convenient option for whining, screaming children ... and I think that's just something I have to resign myself to.
I think educating your children is the key ... educating and tolerance. It may seem odd to them that Dad eats me and Mom doesn't, but that's a great opportunity to teach your children not only your views on the subject, but also about accepting the views of others. PETA has wonderful ideas on how to talk to your children about being a vegetarian, and I plan to do that, so hopefully, when Dad takes them to McDonald's, they'll refuse to eat anything there.
It can work, a vegetarian and a non-vegetarian. It just takes a little bit more work. You need to do lots of talking and discussing before doing anything like getting married or even moving in together, so you hash out all the different scenerios and such, but it can work. My husband and I have been married for almost 2 years, and we dated for 3 before that ... we've never yet had an argument about food or meat.
Good luck to you.