Should bodily injury payouts be included in settlements?

You should be commended for doing the right thing by trying to pay the damages for the accident your husband caused while driving without insurance. It is never wise to drive without automobile insurance, especially when you driving is your occupation.
You are correct that you are responsible for the damages that you caused, but you should only have to pay for those damages which have been proven to be caused by the accident. Most likely, you do not have the knowledge or experience handling insurance claims to adequately know whether or not you are being treated fairly by the other insurance company, or if the amounts they are claiming are proper. Therefore, it is probably in your best interest to contact a lawyer with experience in representing insurance companies and at-fault drivers, so they can properly advise you what information is needed to fairly and adequately evaluate the claim and make sure you are not being forced to pay for something you are not responsible for.
As to having the license suspended, it is a very real possibility. Under Ohio law, it is improper to operate an automobile without insurance. Because driving is a privilege under Ohio law, not a right, the BMV can suspend a person’s license for failing to have insurance and for causing damages associated with an accident without insurance. The BMV can suspend your husband’s license until the damages paid by the other insurance company are paid in full. Probably in your best interest to consult with an attorney so you can make sure your rights are protected while trying to do the right thing.
Best of luck to you.