Your H is so much like mine, being so nice, but it feels like a coverup for the A. My H was doing things to me, calling me, but I know after phone call to me would be a phone call to OW. (that was long time ago, not now). Basically my h was trying to keep both sides happy while he decided. I think in H's mind, it helps decrease the guilt if he can at least make both sides feel not so bad by being nice. Rather than with some other h who would just abruptly leaves.
Long time ago when my h was still in the fog, he told me of course he wanted both. It was only when the fog started to clear that he realized having both was not an option. Even at this point, he does not realize that cutting it off sooner rather than later is a better way for the women (me and OW). But I think he is still a bit selfish in the sense that he still wants both (maintaining contact anyway) even just to lessen the guilt or whatever.