Christmas, Christmas, Christmas,
I made you out of clay,
And when you're dry and ready,
With Christmas I will play.
I am (nominally, by baptism if by nothing else) a Christian; my wife is Jewish. Matters of faith however rarely arise when it comes to our kids. Back when Woody Allen told jokes, he had a pretty good one about how he, an atheist, and his wife, an agnostic, used to have bitter fights about what religion not to bring the children up in. We are taking a similarly hands-off tactic. The pre-school that they both attend has a curriculum which teaches them about Jewish cultural traditions, and that's fine by both of us -- I don't care what religion they reject when they get to be teenagers, as long as they know what they're rejecting.
At home the two holiday traditions co-exist pretty happily. We try to keep the menorah far enough away from the Christmas tree so we don't set the entire co-op on fire, but other than that there have been no real conflicts. And now that the girls are old enough, I've been trying to introduce them to the two holiday television shows that I regularly watched when I was growing up. They're both non-denominational, thankfully, up to a point. At my age, I find that the most disturbing part of How the Grinch Stole Christmas is the condition of the Grinch's teeth, but I don't have any theological quibbles with the show otherwise. A Charlie Brown Christmas is okay too, at least up until the point where Linus goes all evangelical on the gang and offers a reading from the Gospel of Luke, not exactly a part of the Torah (though the Whos weren't a member group of the twelve tribes either, if memory serves).
They're old enough for cartoons, not quite old enough for sectarian debate. This, no doubt, will come. But until then I think A and B are far more interested in the presents than the dogma. That's going to be a tough one. Though Jesus was Jewish, things get more complicated from there. Until then, dad will be very very happy just carving up the Chanukah ham.