Normally if you are married you would want both spouses' names to be on the car insurance policy. It may be up to the procedures of the insurance company however if both you and your spouse will be driving the vehicles then both will most likely need to be listed. If you are listed as the policyholder on both policies then the your husband would need to be listed as a driver for the cars.
As for accidents, if you are involved in an accident with a vehicle which is the spouse's name appears on the registration either by itself or with someone's name, he will most likely be held accountable by the state. As owner (or partial owner) of a vehicle, the state will most likely hold him accountable regardless of who is driving.
As for the driving record, if you are in at-fault in an accident, it will go on your motor vehicle report (MVR). Now, if it is a situation where there is no ticket issued, but a claim gets paid out, it will vary from insurance company to insurance company on how it is handled. In your described scenario, in general, insurance companies will consider it your fault only.
If your husband were to purchase an insurance policy in the future in which you are excluded, then your accident will most likely not affect him. However, with a comprehensive claim some may consider it as a claim for the household - even if she is not listed on the policy as a driver. Again, this will vary from insurance company to insurance company, and you should consult your future insurance company on how they will handle this type of situation.