If you are at all like me I am sure you want to help make him feel better, but sometimes it is beyond our capabilities.
I agree with Tomato that you should continue to be positive, supportive of H, etc.
I don't know if your H is a Christian or not, sounds like maybe since he previously viewed himself 'above' some others (you said something like that anyway) in terms of values/ethics/character...
There is a verse that says "as far as east is from the west", that is how far God keeps your sin away once you ask for forgiveness. I am not the best at sharing my faith, but I know I have told this to my H before. That once you confess and change your ways God takes that choice/mistake and casts if far away from you. So you need to let yourself off the hook.....don't know if that made sense!? Of course your H needs to be able to let himself forgive himself, which you can't make him do even if you wish you could...
My H is also stubborn, doesn't want to go to a counselor despite the fact that he is depressed. I hope your H changes his mind.