Hm, I don't quite see where the problem is.
As far as I understand the facts are these:
1. You went to see a doctor and he performed medical services
2. You are covered by health insurance under a policy held by your husband.
3. You are neither separated nor divorced.
4. Your husband earns money, you don't.
Now, there are some clear legal rules:
1. You obtained the services of the doctor, so the doctor has a right to be paid for them by you.
2. By contract some or all of the costs can be borne by the health insurance. Depending on the contract the doctor can bill the insurance company directly or you can be reimbursed by them. There can be items not covered by insurance, then you are liable to pay for them.
3. If you don't pay the bills the doctor can sue you and collect.
4. Since you are married your husband has a legal duty to support you, in most jurisdictions that means that he has to provide you with the necessities of life to which medical treatment belongs. So if you have no own property the doctor can go after your husband's property.
But why making everything complicated? Why not simply pay the bills if they are fair?