#1 he needs to articulate what he's sorry for: he's sorry he got caught, he's sorry he messed everything up, he's sorry he's been a terrible person, he's sorry you're not waiting on him any more or is he truly sorry and wants to actually make amends?
#2 have you made a list of your demands for him to return to the marriage? If not you should sooner than later. There's a list around here some where, maybe someone can post it, if not I'll try to dig it up later. Mainly it's IC and MC and complete transparency about where the the WH/WAH is going, what they are doing, who they are doing it with, their social media, phone, email, whatever, and the LBS has veto power on things that make them feel uncomfortable.
#3 Most people have a false start some times more than one. Sometimes that leads to Recon, sometimes it doesn't. Take things slow. Don't get your hopes up. And treat H like a skittish cat. Let him come to you, don't go to him.