In a word, no. The only way he can terminate his own parental rights and obligations is to allow your husband to adopt his daughter. That will terminate his obligation to pay support, and his right to parenting time and custody.
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Ms. Gruber is correct. Forget the "rights" of parents - children have the right to have the support of both parents, if they have them. So the only way a parent can voluntarily terminate their own parental rights and responsibilities is for another adult to assume those same rights and responsibilities, by adoption.
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