I can tell you that no, there are no mixed-gender GLBT Choruses here. I am a member of TGMC, and there is also the
Common Woman Chorus in Durham, for women, but both are pretty small (~25 singers) and there hasn't been a demand for a mixed-gender one yet (though we have done joint concerts before, and in fact, I believe may be doing a joint concert this coming spring). What's wrong with the two of you joining separate choruses? They rehearse the same night.
If "mixed" trumps "GLBT" for you, then pretty much any of the community choruses here would be fine, depending on where you are. The Durham Choral Society and the Master Chorale (rehearses in Raleigh) both have PLENTY of gay members, I know for a fact, but they don't perform at events such as Pride, etc.
The closest mixed GLBT chorus to here is One Voice in Charlotte.
PM for more info if you want.