The photo was used in mailers in a June primary election that included Sen. Jean White, one of a handful of Republicans who supported a civil-unions bill blocked in the Colorado House. The mailer replaced the New York scene with a snowy background and read: "State Sen. Jean White's Idea of 'Family Values?' " White lost in the primary.
Public Advocate of the United States did not respond to two e-mails seeking comment.
The Southern Poverty Law Center announced that it would take legal action on Wednesday, saying Public Advocate used the couple's photo "without permission and altered the image to include antigay propaganda."
Edwards, 32, is a college administrator, and Privitere, 37, is a ticket broker, according to an interview. They have been together for a dozen years and married in Connecticut.
It was not immediately clear what relief they were seeking. The photographer is a plaintiff in the lawsuit.
The couple also is suing over a Public Advocate mailer that used the photo in a Colorado state race that involved a Republican who was not in the Legislature when civil unions were considered.
A bill that would have let Colorado couples enter civil unions passed the Democratic-controlled Senate this year, but was defeated in the Republican-led House with a filibuster. Democratic Gov. John Hickenlooper supported the measure.