It's a good idea to write down an idea of what it would look like, if H was REALLY a good guy who was SERIOUS about making amends (you don't wasnt him back if he's not, right?).
A good guy who saw the error of his ways and really wanted to make amends, would have the OW out of there pronto. Would go to marriage counseling with you. Would agree to live on his own for 6-12 months while you date each other. Would be willing to give you complete transparency (access to phone records and email, for example).