If you can’t seem to find it there, it may be listed on the car’s registration, although that is less common in most states. Contacting the family friend that lent you the vehicle would be your best bet if all else fails.
If you cannot get in contact with the owner of the car, you might have some luck with the Department of Motor Vehicles (DMV). Usually, they keep a record of whether or not a vehicle is insured. You can call and request to know if the vehicle you are borrowing is insured, although you’ll need to provide your contact information, reason for the request, and some way for them to verify your story. Even with proof provided, the DMV can deny your request if they feel you’ve given false information, so make sure you have everything in order.
Best of luck, and enjoy hitting the open road again!