Home insurance covers many things, including your personal property. The policy will also pay for claims on your property when it is located somewhere other than your home, but there are limitations on when and how you file this type of claim.
If you store property in a storage unit or facility, you are also assuming the burden of risk for your property. Home insurance will not provide coverage for items that are stored at a location other than your home. Instead, the burden belongs to you, the owner of the property, or a separate personal property policy. With a storage facility, you will have to sign a waiver of liability with the property owner when you purchase your storage space.
The storage facility may offer you a specialized insurance policy for your storage unit. The details of the policy will differ by facility owner; state where the facility is located, and the insurance company which underwrites the policy. In this case, the policy may have limits which discourage the storage of high value items.
You can purchase your own personal property policies, and may even qualify for a discount on the coverage if your property is stored in a facility which provides 24 hours monitoring of the site. Since the facility has removed a large portion of the risk involved, insurance companies will have lower premiums to compensate for the lowered expected claims rate.
Although homeowners insurance protects your personal property, it is not intended to be a complete insurance solution. The idea of a standard policy to prevent your family from suffering a total loss if everything you own is suddenly destroyed by a covered peril, such as a fire or major storm. Extending the protection to cover your personal property stored at a storage facility would drive the cost of premiums beyond what you might be willing to pay.