What About the Children?

My wife and I met exactly two years to the day before our wedding, and had known each other for about twenty minutes before the topic of future children came up as a tangent of a seriously FASCINATING discussion on religion. Twenty minutes into the rest of our lives, and she made it abundantly clear that her future children would be raised Jewish. So how can I pass on my faith to my children, when I already swore to my wife that I would raise them in the manner of her ancestors?