I'm going to insert my experience here although the situation is not exactly the same. From a man's point of view he is living in a sexless marriage ? Is that correct ? Is it also emotionally deficient on your part ? Do you have a physical connection ?
Do you still have a passion for him ? Or do you view sexual activity a chore. I. Know that my wife wouldn't care what I do on the outside as long as I leave her alone. She cannot have sex with me on any level due to physical reasons. Yet I think her blockage is psychological. Doesn't want therapy. I would do anything to meet her needs , but she won't do that for me. What am I supposed to do ? Luckily I don't have children to take care of. BTW : I suffer from severe chronic depression. I do my best to function normally but it is not easy. That's all I can say for now except , don't give up on him. He doesn't really want to go outside the marriage for sex , it seems he has no choice. It's a need that has to be fulfilled.