As a spouse in a same-sex marriage, I suggest spouse as a valuable term for any people in a marriage, regardless of gender(s). When we got married, the celebrant congratulated us as now being " husband and husband."
The difficulty with "partner" is that is is ambiguous on whether it is a familial term or a business term. Even after being married for 12 years and in a domestic partnership for almost 20 years, people newly met and told that we are partners still assume my spouse and I are in business together.
Also, we are married AND domestic partners - two different statuses, entered into at different times, and still both applicable. At one time, before national marriage equality, being domestic partners could provide rights in states that didn't yet affirm same-sex marriage.
Thanks for thinking about all this.
San Francisco, CA