You will need to file a Petition for Termination. Terminations and adoptions are fairly complex matters, often requiring other steps (ad litems, home studies, criminal background checks, etc.) that vary from case to case and Court to Court. I'd recommend hiring a local family lawyer to assist. Furthermore, some Courts won't grant a voluntary termination without an adoption, so it might be necessary to file a Petition for Termination and Adoption, even if you only complete the adoption when your current husband returns from overseas. Again, another reason to consult with a family lawyer in your area.
I'd like to note simply because one gives up parental rights doesn't mean that the court will cease child support. Here it appears that you want your child's father to terminate parental rights in order to get out of back child support. I'd guess that it is likely that your child's father will agree to this.
You do have other options besides adoption and termination of parental rights. You probably want to talk with an attorney in your area to understand the different routes.