A common misconception is that the state of residence must approve same-sex marriages in order for a domestic partner to receive the same benefits as a spouse. The fact is that domestic partners are both same and opposite sex living arrangements. Where health insurance is concerned, the decision of whether to insure domestic partners is not even a legal one, with many insurers choosing to accept domestic partnerships while others do not.
If an insurance company does make arrangements for domestic partners, there is still no guarantee that the employer will do the same. Since many employers pay a percentage of the cost of health insurance for their employees, they retain the right to limit who, beyond the employee, they will extend the benefits to. If the employer does offer coverage for domestic partners, it must be equal to the coverage offered to married partners. The employer makes the decision of whether spouses and domestic partners are covered, but cannot choose to offer different coverage plans for the two.
You and your partner may be required to sign an affidavit for the insurance company. This affidavit would state that the two of you are living to together in a co-beneficial relationship and that you intend to remain together for an extended period of time. This is required by insurance companies to prevent friends and roommates from taking advantage of the domestic partnership in order to get insurance coverage and other benefits.
If your employer does not offer coverage to spouses or domestic partners, but does pay a portion of your own health insurance proceeds, ask the employer if they will allow your partner to participate if you pay the full premiums for them. This would allow your domestic partner to join the plan without any additional cost to the employer, eliminating the primary argument against allowing them on the policy.
If your state legally recognizes domestic partnerships, you employer and insurer must do so as well. Neither party has to make any special arrangements for domestic partnerships, but the available benefits are required to mirror the benefits offered to opposite-sex, married couples.