Married to non Muslim

Assalamu Alaikum everyone.

First let me say that openly that I won't leave my husband. I love him very, very much. We have a wonderful relationship.

I am a new Muslim revert. My husband is not Muslim. He was raised Catholic but doesn't practice any religion currently. I've been reading online and I know it's prohibited for a Musilmah to marry a non Muslim. But I am a revert. I found Islam many years after we were married (in a non religious ceremony.) Again, I love my husband very much and absolutely don't want to leave him.

He's not happy about my reverting. He has a very typical and misinformed view of Muslims as a whole (terrorism, etc. etc. etc. ) He recognizes it as a beautiful religion which teaches a wonderful way of life, but he wonders why there are (his words) "so many zealots and crazy people in Islam and not other religions." Of course I pointed out that there are over a billion Muslims, it's unfair to judge them all by the actions of a few crazy people.

But here's the thing. He has an immense and powerful belief in God. We share exactly the same morals and values regarding God (and everything else) I spoke to him about converting, but he's so blinded by his misinformed understanding of Islam that the thought is really something he won't consider. I told him about the shahada- that if you believe that there is no God but Allah (swt) and Muhammad (pbuh) is His messenger, then that is what it means to be a Muslim on the most basic level. I asked him if he believed that and he said "Well of course" and then with a huge laugh "but I'm not Muslim." See, his core beliefs are essentially Muslim, even though he won't admit it.

Is it permissible for me to stay with him while continuing to try and teach him what little I know and try to lead him down the right path? Knowing that he believes the same as me but he just won't say it for fear of being judged by the world (??) can I stay with him and show him that his misconceptions are just that- misconceptions?

And what if, with time, he realizes that he's being stubborn and takes his shahada. Maybe he doesn't fulfill all of the requirements of being a "good" Muslim, and maybe he never tells a single soul except for me, he's still Muslim, right? If someone believes in their heart the words of the shahada, they're Muslim. That's what I've been told.

Is this a horrible, unforgivable sin? I want him on this journey with me, and I'll do just about anything to make that happen.

Sorry for the brutal honesty, but this has kind of been eating away at me for a while.