Chances are that your stepson didn't say he wanted to be adopted by his stepdad. Or they would have had him talk to your husband.
Your husband does not have to sign any adoption papers. Unless his ex can prove him unfit, she's not going to be able to terminate his parental rights.
As for the child support, if the stepfather adopts your stepson, then there isn't any. By adopting his stepson, the stepfather takes on the financial obligation. If your husband decides to let the stepfather adopt his son, then he should make it clear that there will be no child support.