Your H just sounds like he wants the proverbial milk for free, IMHO. Maya Angelou has a quote that I love: "The first time someone shows you who they are, believe them."
Your H has shown you the man he is over and over. Believe him. You have too much value to choose to remain in that situation. I'm going to say something that may sound harsh...but it's not meant to be an attack. I had someone say the same thing to me once, and once I got over being upset, I realized it was true.
If you continue to spend time with your H and listen to his crap, YOU are choosing to abuse yourself. Your H has shown who he is...it doesn't excuse his jerkiness, but at this point, you are the one hurting yourself, not him, because you could elect to walk away from anyone who shows so little respect for you.
On another note, I sort of understand the warped logic of getting rid of the piece of paper. Now, I don't think your H is saying that for any other reason than to keep you on the line and keep you hoping while letting go of any personal responsibility, so this doesn't apply to him. However, back when my sitch was going on and H and I had reconciled, my trust in him and in the institution of M was so broken, I kind of wanted to do the same thing. The piece of paper didn't keep him from pursuing an OW or staying committed to working on our R, so why keep it? I actually said that to H, and he blanched. In some ways I still feel that way, and I actually probably work from the belief that being married--or not--has little impact on the quality of my R...which is a good thing. I don't take it for granted anymore.
Don't sign over the house to him. Make him work.
SD
Me: 40 H: 43 H had EA from 2/06-9/06 Bomb 5/06 Piecing since 9/2006 3/2008: Boundary setting 7/2009: Boundary crossing~dropped my own bomb. 8/2010: Marriage finally on track!