I don't usually weigh in, but I will this time.
I am sorry EWallace. I do understand how you feel. My husband was a fallen away Catholic. I was always Southern Baptist and a few other things. We married in the Baptist church. He wished to return to the Catholic church. I eventually followed and even found the traditional mass years later. Hubby, however, does not go to any church now, and does not consider himself Catholic. I won't bother listing the many euphemisms he extols to such people.
So, you see, I am in a similar situation being a Catholic with a "Baptist" or basically a non-believing husband. I got there through no fault of my own, he just changed somewhere along the way. Well, I did as well. Or I like to think I found myself and the faith I was looking for all along. Not that that matters. The point is, other people sometimes find themselves in similar circuмstances, not through any fault of their own. It is a cross we bear no matter how we got here.
And crosses are rarely, easily undone.
And unfortunately, your situation is not likely to get better. Protestants, non-Catholics, agnostics, whatever they are - they are operating on a different playing field with a different level of equipment while facing the world. There is no way to "fix" such things unless he converts. All you can do is play out the deck you've been dealt (or in this case chosen) and do so by God's will (his will being doing according to what he has decreed is lawful and just and clear for you to do) and let the chips fall where they may. If that means your husband leaves, so be it. If he converts, you are truly blessed. If the status quo remains, you keep praying. I know that is stressful and hard to hear, but it is where you are at right now.
Believe me. I know of what I speak. I have been doing this sort of thing for the past 15 or so years, ever since I first entered tradition. In fact, my husband once told me when I refused to go back to the Baptist church or take the kids there - "I wish I had never taken you to that Catholic Church." And it was said very ugly and harsh and full of venom. We have argued about sex. We have argued about homeschooling the children. We have argued about money. We have argued about just about anything you can name, simply because my vision of life is Catholic and his is not.
And yes, we are still married. Some times are better and okay, others are not. I will say that even as Protestants, neither of us believed in divorce, so that is probably the biggest reason he is still in the marriage at the moment. To be honest, I remained many times because of my Catholic faith. Had I still been Protestant when some of these issues first surfaced, I would have found a reason to justify leaving. My perseverance in this marriage is truly due to God's grace. I have a college degree and worked for many years before I married. I could have easily walked out, taken the kids, got a lawyer, and gone back into the workforce. But I chose to stay.
I will close with another thought, and it is not any of my business I will grant you - however, I noticed you have been married for 3 years but you have no children. People, of course, do have trouble conceiving, and perhaps you go to a Novus Ordo church and I am aware that many Catholics there use natural family planning to avoid pregnancies. I am not trying to be harsh with you, but merely am wondering if this is yet another bone of contention? Does your husband embrace the Church's teaching on life? Do you? Being married, but avoiding a pregnancy, blankets your marriage with a sense of selfishness and creates another set of problems in opposition to God's plan for marriage.