If he's willing to let go of the house (ie, a quit-claim deed) without demanding equity, and the rest of it is as you described before, then run those papers by a lawyer and sign them quick. Is he on the mortgage? If so, then he is still responsible for the debt even if he quit-claims the property to you. Normally you would be required to re-finance to remove his name. Alternatively, you can agree to a "hold harmless" clause in the settlement (you take full responsibility for the debt).
At this point I think he is still feeling guilty, and therefore inclined to be "generous" to assuage that guilt. That will eventually change.
