So why have you not insisted on transparency? Are you afraid of what he will say or do? Just curious.
I understand how you are choosing to respond and that's certainly one way to go. Personally I think that's the way to respond to someone who has been acting honestly. If you know that your H has been lying to you why would you let him continue to cross this boundary without consequences?
I'm not trying to judge, just maybe look at things differently to help you get unstuck.
If you love somebody, set them free. http://tinyurl.com/2empx2g