My ex agreed to sign over his rights ot our daughter and my husband is going to adopt her. He will no longer owe CS but I also want to make it so he owes no back CS. We both want to go out separate ways and get on with our lives. Is that possible?

Maybe, your attorney who is drawing up the adoption paper work ( do not do this without an attorney) should include that in the paper work where he is signing over his rights.
The judge may not allow it, The judge will have the final say on this, Many times the judge will require him to still pay the past due support and may even want a garnishment of his pay for it.

I agree with Chuck, but a key here is whether you ever use public assistance. If you did, the state is likely to insist on being repaid. If not, a judge is more likely to allow it.

Scott is correct I forgot about that issue, Yes, if the custody parent or the child got any type of welfare and/or assistance, then the state itself has a claim to support.