The country singer and Cibrian were married to other people when they met on the set of the TV movie "Northern Lights" in 2008. They ended their respective marriages the following year and were married in 2011.
Cibrian's ex-wife and mother of his two young children, "Real Housewives of Beverly Hills" star Brandi Glanville, has been critical of his relationship with Rimes since the beginning.
Rimes has repeatedly said in interviews she was upset by the public perception she was a home-wrecker and is eager to restore her image.
"We're doing a TV show based on our reality," Rimes told People.com Thursday.
"We'll take things out of our lives and elaborate them and make them funny. People have been laughing at us -- we want them to laugh with us!" she said. "For some reason, everyone is so interested in our lives but they don't actually know about them. ... What they read is what they see. We want to be able to take control of our lives again so we want to do a show about us, about our lives, but scripted."
Rimes doesn't have a title or network for the show yet, People.com said.
Her latest album, "Spitfire," is due out next week.