There may be two different issues here, one that you live in the same household and thus his insurance company is turning down your claim due to a household exclusion in his policy and the second issue concerning that you live with your boyfriend and that they were unaware of this and had not added you to his policy.

Most insurance companies require that all licensed drivers in a residence are listed on a policy or at the least the insurance company is notified of drivers living in the household and will inform you if they all must be added to the policy or not.

As for the damages to your vehicle in this situation, some insurance policies have what is referred to as a "household exclusion" meaning that if say the driver backs into another household car in the driveway, such as your boyfriend did here, that the liability insurance will not cover the accident.

The mandatory liability coverage on your vehicles protects members of your household against claims brought by people who are NOT part of the household normally, thus if a household car has been damaged it would not usually be covered under your liability policy.

To find out for certain if this is the reason why your boyfriend's insurance company is not allowing you to place a claim for your damages ask for more information on the denial and have your boyfriend read through the policy to see if he finds the household exclusion in it. Your state's insurance regulator should also be able to explain more about your situation and this exclusion.

Not all insurance companies have this type of exclusion as part of their policy so you and your boyfriend may want to shop around for different insurance coverage. If his insurance company definitely will not cover your damages then you could place a claim against your collision coverage, if you have it, or ask for your boyfriend to personally pay for the damages he caused to your vehicle.