Does the non-custodial parent have to pay all of the childs medical bills?

My husband has a 9 year old son that lives 3000 miles away. He has only seen him once. There was a question of the paternity and my husband never found out that he was the biological father until the child was 4 years old. My husband pays 70 dollars weekly in child support and has never missed a payment. We are able to check online at his account and his payment history and its shows that he owes $993 in rears. My husband does not have health insurance so every time his son goes to the doctor or emergency room or dentist or anything they put the bill on his child support and it puts him behind again. The mother has sent nasty letters, text messages, and emails and said that he is not allowed to see his son. We were planning for vacation next month and would go to her town to visit but she will not allow it. He called and spoke to the local child support enforcement and they told him to file for a modification and request to sign off his parental rights and he can go before a judge and it might be dismissed and he wont have to pay child support or his medical bills. I am wondering if this is even possible. I've never heard of being able to just sign off your rights and not have to be financially responsible for the child anymore. Also when my husband was laid off work, only for one week he missed, he called and texted saying she was calling the DMV to suspend his license. He got a job the very next week and started sending his payments again and then she left him alone. Would it be a good idea for him to try this modification since they are 3000 miles away and he is never allowed to see him anyways because the mother refuses even though he pays child support. Anyone in a simalar situation or any advice would help. PS we have been together 7 years and have a 4 year old son together and money is tight right now.