If you have health insurance, it's usually no problem to provide added coverage for your spouse. With domestic partners, it depends on the employer. Many companies won't grant your unmarried partner, straight or gay, the same benefits a spouse gets automatically. If you don't know your company's policy, ask your employer's HR department for the facts.
Since 1982, when the "Village Voice" became the first private employer to offer domestic-partner coverage, thousands of companies and many state and local governments have provided health insurance coverage to domestic partners. Some employers only offer coverage to same-sex domestic partners. The thinking is that if heterosexual couples wants insurance coverage, they should go ahead and get married. The majority of employers who offer domestic-partner coverage extend it to both straight and gay couples, however.
If you share benefits with your spouse, you can show your employer's human relations department your marriage certificate to prove his status. When you apply on behalf of your domestic partner, HR will probably want an affidavit swearing to your status. Typically the affidavit requires you to confirm that the two of you live in the same house, that you've done so for six months or more and that you share responsibility for living expenses. You can share responsibility without splitting them down the middle.
If you want domestic-partner coverage and your employer doesn't offer it, work with other employees to make a case for change. The Alternatives to Marriage Project website links to several guidebooks on how to persuade your employer to change company policy. Some opposite-sex couples at companies that only grant benefits to same-sex arrangements have tried suing, claiming discrimination. As of late 2012, that hasn't been a winning tactic: No judges have sided with the plaintiffs.
As of 2010, you can also cover your adult children under your policy, at least until they turn 26. Before the passage of the Affordable Care Act, it was legal for employers to cut off kids' coverage once they turned 18 or 21, and many health plans did so. Under the new law, your kids can get coverage even if they don't live with you and you don't claim them as dependents. It also doesn't matter whether you give them any other financial support. Some employers say they're increasing plan rates for employees who register multiple dependents.