Depending on the company you use and the state you live in, it may be possible to add a spouse rider to your policy which covers your domestic partner. Some states recognize same sex partnerships, and some life insurance companies recognize them even in states which do not. You will have to do some research in your state of residence to determine what your options are in that state, but you can get the coverage you and your partner need.
Domestic partnerships are being recognized more widely, especially now that some states allow same sex marriages. In states where they are recognized, insurance companies write spouse riders for domestic partners. Insurance laws are regulated at the state level, and spouse riders must conform to the laws. States which recognize common law marriages generally make allowances for domestic partnerships under the rules governing common law marriages.
However, some insurance companies will recognize same sex partnerships in their own right, providing spouse riders to partners who meet certain qualifications. The partners must verify residential requirements, and may need to show proof of financial partnership in the household as well, such as joint bank accounts, lease or mortgage payments, and shared maintenance of the property and associated utilities.
The requirements will vary from state to state and between different insurance companies. If your current insurer does not provide a spouse rider for your situation, try shopping online for insurance quotes from companies which do. Do not assume that simply because one company does not have this option that it is not available from other sources. Spouse coverage and riders are available in one form or another in most states, so your only task to find a company to fill your needs.