Brokeback marriage
n. A current or former marriage in which one partner is gay or has had a gay affair.
Mrs. Remmele — now married to a farmer who raises cattle, corn and soybeans — is one of an estimated 1.7 million to 3.4 million American women who once were or are now married to men who have sex with men.

The estimate derives from ''The Social Organization of Sexuality,'' a 1990 study, that found that 3.9 percent of American men who had ever been married had had sex with men in the previous five years. The lead author, Edward O. Laumann, a sociologist at the University of Chicago, estimated that 2 to 4 percent of ever-married American women had knowingly or unknowingly been in what are now called mixed-orientation marriages.
—Katy Butler, “Many Couples Must Negotiate Terms of 'Brokeback' Marriages,” The New York Times, March 07, 2006
We are ecstatically happy together. This is no Brokeback Marriage!
—“An Army of Davids Attacks Barry C. Lynn” (photo caption), Wonkette, March 07, 2006
2006 (earliest)
As she’s strolling toward the altar, Rachel gets a look at Luce (Lena Headey of Terry Gilliam’s "The Brothers Grimm"), and — whammo — it’s "Brokeback Marriage" time.
—James Verniere, “'Imagine' a sappy Sapphic flick,” The Boston Herald, February 03, 2006
From the movie "Brokeback Mountain," about a gay love affair between two cowboys, both of whom are married.