Victoria W said it all...
Child support isn't paying to see your child, it's paying for your share their care and raising.
Even if your SS was 45 years old... if there was 10 years (or 5 or 2) of back support owed by your husband, he would still be legally obligated to pay it to his XW, just like any other debt. She supported him on her own for years, when your husband had a legal and moral obligation to be contributing.
Child support orders vary enormously. Some end at 18. Some end at 22 or 24 or at the completion of a bachelors degree. No matter what, your husband owes the back support. He may still owe currently for the next several years depending on the order.
To find out the details, consult with an attorney.