A mixed orientation marriage is a marriage between a man and a woman, in which one of the spouses is gay. The term itself, like so many terms relating to the gay-and-christian conversation, is somewhat controversial. I’m personally fine with it, and Anna and I use it on occasion when sharing our story.
Below is a link to a helpful resource to get you up to speed on m-o-ms. There, you’ll find additional links to articles from several people, including me, who are in such marriages.