I think you're worrying too much. In my atheist family us kids were allowed to watch all the Christmas shows we wanted, and it never instilled a burning desire in us to go to church. Christmas is a great holiday -- the lights, the smell of the tree, the Santa myth, sitting around the tree giving and getting presents with your loved ones. You don't have to celebrate if you don't want to, but I think it's entirely possible to incorporate it into your tradition as an American family no matter what your religion.

Have a little faith in your kids. They'll be smart enough to figure out the difference between your religion and a nice holiday that can mean different things to different people. I'm glad my parents did.