Seen you post on my thread .. and I just caught up on yours. To be perfectly honest there is not much detail in your thread to really know if you are piecing or not. Seems your H is attempting to be more transparent, but you have reservations ... I can understand both.
My W has been trying very hard, very remorseful for the A (which I am aware is rear for a MLCr) and we are very slowly trying to reconnect and fix the issues that took YEARS to reach a all time high that resulted in destroying our marriage.
I will say this ... your H seems interested, you are unsure. I am not picking up if either of you go to church or what your day to day interactions are ... only that H is sleeping on the couch .. but not certain whose idea that is. For my W and I communication became a big problem, we attended Retrouvaille a few weeks ago and it has been a very big help thus far, I do not know enough about your sitch to know if this would be a good thing for you and your H at this point, but I would suggest somewhere you get some help communicating.
I think your H discovered he has to earn your trust, its a slow process but it does appear he is trying.