More: Slavin and Korte said the alleged insubordination cited in their termination notices was related to interviews they gave to CBS News for a piece on "CBS Sunday Morning" that aired in July. In the story, Korte said that she worked for Stars and Stripes, "not for the Pentagon, not for any administration, not for any policymaker."

More than a month later, the newspaper published a piece detailing flagging mental health and food and water shortages aboard the Lincoln, which has been deployed for nine months. A day after that story ran, the lawsuit says, the defendants "ordered plaintiff Max Lederer, Stripes' publisher, to present notices of separation to Mr. Slavin and Ms. Korte."

"The notices charged them with insubordination for the statements they made five and one-half weeks earlier on 'CBS Sunday Morning,'" the lawsuit reads.

He did not deliver the notices. Lederer announced his intent to retire at the end of September over "fundamental" differences with the Defense Department, but the Pentagon fired him before he could.

The three fired staffers' complaint says they are "facing imminent retaliation and termination in violation of their First Amendment and statutory rights."

"This action seeks to prevent the blatant violation of the First Amendment rights of these journalists and challenges the U.S. Department of Defense's ("DoD") extraordinary censorship efforts in violation of both the First Amendment and DoD regulations and policies," the lawsuit reads.