Typically even without having insurance on your car, your husband should be able to make a claim against the at-fault party's auto insurance policy for the damages to your vehicle.
There can be some confusion in terms. Typically, if you drive without having your license on your person then it is a traffic infraction with limited fines ($35 to $150, depending on the state). Read below to learn more about driving without a license because of suspension, revocation, etc.
As for the penalties for driving without a license or insurance, they are usually quite serious in Arizona. Driving without a license is a class 1 misdemeanor and penalties can include the vehicle being impounded, 48 hours in jail and a court imposed fine of $300 or more.
If you do not have insurance the in AZ, the Motor Vehicle Division may suspend your license plates and registration. To reinstate these privileges, fees and future proof of financial responsibility must be filed with the MVD. The future proof requirement is most commonly an SR22.
If at the time of that accident you had auto insurance but did not have proof of it in the vehicle so were cited, you can show proof of valid insurance for that time period and have the citation dismissed. However if you do not show proper proof of insurance, the judge may issue a fine in addition to any action taken by the MVD.