"What happened is not who I am, period," the Grammy winner tells ABC's Robin Roberts in Wednesday's All-Access Nashville special. "But I do know how much I love him. So I've always said I don't live my life with regret. I can't."
Rimes met Cibrian last year on the set of their made-for-TV movie Northern Lights. At the time, Rimes was married to Dean Sheremet and Cibrian was married with two kids to Brandi Glanville. Rimes and Sheremet separated in September 2009 following reports of her extramarital relationship with Cibrian. The divorce was finalized in December and she moved in with Cibrian, who divorced Glanville shortly thereafter.
"It happens every day to so many people," Rimes says. "You had two couples whose marriages didn't work who really stumbled upon each other and fell in love."
Cibrian adds: "We're talking about something that's over a year, year and-a-half old, really, and we're still together and we're madly in love. And I think people are finally seeing that, but it doesn't mean that people will accept it or the tabloids will stop trying to print lies and try to tear us apart or tear us down."
In the Spotlight with Robin Roberts: All-Access Nashville airs Wednesday at 10/9c on ABC.
Watch a clip of the interview below.