Sorry to be answering this question so long after you wrote it, but I just got connected to this service.  Yes, if your husband and his ex-wife agree, they can enter an Agreed Order that terminates child support.  You will have to let the court know why that's happening (a "step-parent adoption" is what you tell the court and that's short-hand for the situation).  About your husband "giving up rights", does that include no more visitation with his children?  If so, I'm not sure I would want to sign that.