As cited above, the Shulchan Aruch advises against it. The Mishna in Kesubos talks about divorce if it's discovered that a spouse is non-observant, and/or the non-observance is affecting the observant spouse. (More on that in a moment.)
Let's start with two important points here:
(Let's also remember the Gemara says don't go into a marriage that is likely to lead to resentment; "love your neighbor like yourself" applies to your spouse too.)
Rabbi Mordechai Willig shlit"a has a YUTorah mp3 on Kibud Av V'em where he addresses the obligation of respect (broadly) towards a non-observant parent. In the course of that, he remarks: Chazal also say you have to respect your spouse. Today it would be scandalous, but not long ago it was not uncommon -- suppose one spouse is observant and the other isn't; does that mean he doesn't have to respect her (or vice versa?)
The really big questions that will need to be asked are how the kids will be raised, and what about things that affect the other spouse -- most notably "family purity" and "is the food in our kitchen kosher?" (This can get a drop trickier when we address the question of "can I trust a person who doesn't keep kosher to keep my plates kosher?")
Long story short: it's generally not the greatest idea, but with a lot of agreement and planning, it could be doable. There doesn't seem to be a clear thou-shalt-not against it. The least-problematic scenario would be something like a second marriage in which the kids are out of the house and Nida is no longer a biological concern.