Your husband sounds sincere in that he WANTS to do this; however, at this point you need to be skeptical (for your own sake) about his ABILITY to do it. This means putting some emotional safeguards in place for yourself.
I don't have time to get into ALL of the details, and since my posts are still "fully moderated" I'm not even sure you'll see this, but four things I would STRONGLY encourage:
1. Your husband needs to send OW a no-contact letter, the content to be approved by YOU, and you should deliver or send it (so that he doesn't add or subtract anything).
2. He needs to be fully transparent with you. This means changing his cellphone number (so that OW can't contact him) and the detailed billing coming to you, keeping it unlocked and available to you any time you want to look at it, changing his e-mail address(es), etc.
3. Marriage counseling with someone specifically trained in dealing with infidelity.
4. A full-panel STD test, with a copy of the results going to YOU.
As for him moving back in, I would strongly advise against it just yet. Let him maintain his own place for the next 3-6 months (I'd recommend six), while maintaining NC with OW, and he can date you. TAKE IT SLOW. This is healthier for him AND for you, as he can have some space to learn to deal with why he deals with his marital dissatisfaction in unhealthy ways (preferably with the help of a good IC), and you can view his changes (and his new fidelity/NC) from a healthy distance.
I've been studying affairs for over six years -- literally thousands of them. I've never seen successful reconciliation work without most -- if not all -- of the above. If you do these things, however, and if he's sincere, then you have a good chance at success. Let him run back to you too easily, however, and without these safeguards in place, and the recidivism rate for another affair is well over 90%.
