He can only terminate his parental rights and thereby terminate his child support obligation if your new husband is adopting the children. Since you do not mention this, I assume this is not the case. He could ask for some parenting time. Given what you describe, I expect that time to be very limited. If granted, it probably will be for just a few hours at a time here in Colorado. It might even have to be supervised at first. I recommend you persist in your collection efforts and deal with the parenting time issues if/when they arise.
Sign up to receive a 3-part series of useful information and advice about child custody law.