Thanks all for the replies. I would like to give more information in the hopes it can shed more light on this complex and heartbreaking situation.
First, my husband has come a long way. When I first met him, he was completely numb to everything: joy, happiness, love, death, grief, mourning, anything. He was cold as ice and nothing affected him. I could sometimes see vague flashes of something but it would be tamped down immediately.
After years with him in this state, I saw him genuinely cry for the first time. He is an emotionless person and it is easy to tell when he is faking emotion. This was the first genuine spontaneous emotion I ever saw in him and he was clearly unable to suppress it. It happened when I was talking to him about God; he had displayed interest in learning more as he believed nothing else could help him and I obliged. I myself was feeling very cold and distant that day, feeling very hurt and tired of the whole thing and thinking there was no point. He later could not explain this sudden rush of emotion and said it was nothing he had ever felt before, and he could not even name it. He just knew it was good. He had a second such experience when we got in a big fight and I left the house. He suddenly felt a strong draw to a particular part of the house, where I had placed a just-purchased artwork displaying a Christian verse. He did not know I had bought it or that it was there, so he picked it up to look at it. At first the words were meaningless to him and then he said it suddenly made complete and perfect sense in that moment, and the tears started pouring again.
I believe these two experiences were God-given and miraculous. It is unfathomable that he could even experience something like this and I believe it is a testament to the power of God's love and grace. However, I know that doesn't mean he will necessarily change. As a sociopath there are fundamental physiological differences he was born with, coupled with poor genetics and bad upbringing. It just seems so unfair that one would be born like this with no chance of change. There was no instant transformation afterwards and he still struggles with the same problems, but he claims to really want to change. He acknowledges having a lack of empathy, emotions, and morals/conscience but says he does not want to be like that anymore because he is losing me. This past week he actually contacted some psychologists/psychiatrists but I do not know if they can even help. I am a medical professional and I know there is no effective treatment or medication for this personality disorder.
What should I do? I plan to meet with a pastor this week but I've talked to some in the past and they were no help. I trust God completely and I just want to do His will.