After MLC, do they understand their behavior?

[canadianMrs.]

I'm not sure how to link a thread, but its under MLC as "empowerment over, I just had H pack his bags"

Bascically, the last 2 weeks I have seen my old H more and more. He has been over 12 out of 14 days. A couple times he came over when the kids were in school "to borrow something" but would linger and try and get a conversation going. I could feel he wanted to say more or have me say more. He has been more involved with the kids. When I do call/text him about the kids, he respons right away. He has been doing little chores around the house when he is here, without me asking. Friday he came to pick up the kids and we ended up standing in the yard for over an hour talking. He told me that he never had feelings for OW,she was more like a security blanket. He really did think he was working on our M, but realizes now you can't with a 3rd person. He says he is filled with regret and guilt, and he knows the aftermath is not over. (The kids & I are moving to our home town in July). H has to stay for now because of his job, but he has told me 3 times in the last week he is looking to transfer. A few months ago that was never an option with him.
So I'm seeing progress, but he doesn't seem to understand fully why he let is happen, go on as long as it did, the lies, or why he couldn't tell me when I gave him lots of chances. I did get more answers this time, then I ever have though.
Friday night he texted me to tell me he misses me. Last night after talking to the kids he asked to talk to me, and just asked about my day.
I'm so confused. I feel myself getting my guard down. I know I still have to move. To much has happened here, and I've never been happy in this town. I need to go home to get my life back. On the other hand, do I let H back in? Now? Later? Do I say anything or I just continue to see what happens? I've always been the one to do "temperature readings" for our R. H is not a talker and not good at expressing his emotions. I feel the ball should be in his court, but knowing him, he wouldn't know where to start.

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I hope I don't get in trouble for this, but I might put this on my other thread too, as an update.