I'd like to chime in from the H's point of view. I don't know if this will help you, but reading your post has helped me. So, I am compelled to contribute.
In my case, I work very closly with the OW, and struggled with the same pattern as your H. As it was explained to me, and what is finally helping me break the cycle, is that the OW is an addiction, and like any other addiction, recovery is riddled with pitfalls. A luring glance, comment or even an email would cause me to stumble when just the night before I was distraught with remorse and determined not to stray again. It's a difficult hurdle to overcome. H needs to deal, honestly, with the reasons that caused the A. Keeping the OW out of the equation. When things clear up, I'm betting that he will see the OW for what she truly is.
Best Wishes, mike
"Just as there is a calm before the storm, there is also a storm before the calm."