Us Weekly first broke the news that she and Cibrian, 37, had an off-camera fling last year while shooting the Lifetime flick, Northern Lights. At the time, Rimes, now 28, was wed to dancer Deane Sheremet; Cibrian was raising two children with his wife, model Brandi Glanville.
"It happens every day to so many people," Rimes says of the affair. "And if I take away my album sales, my words ... you have just another couple. You had two couples whose marriages didn't work who really stumbled upon each other and fell in love. I can't change [critics'] minds. Nothing I'm going to say is going to change it. I do know that and I have accepted that."
Cibrian also chimes in, opening up for the first time about falling for Rimes.
"The truth is that we're human beings," he says. "We make mistakes and we learn from them, but we're human. We fell in love.
"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," he goes on. "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."
Adds Rimes, "We're really happy in what we feel privately. We hope [that] one day, I think people will feel publicly."
Contrary to Internet reports, Rimes doesn't break down in tears talking about the affair. She cries when asked about her book, What I Cannot Change, in which she writes that there was once a time when, if she wasn't doing a show, she didn't know what do with herself.
"That was my life!" she says, crying.
"I'm learning who I am without it and that's the coolest thing about my life right now, that I have all of these incredible things happening, and I have family and -- and I'm learning who I am without it."
These days, Rimes says music isn't the burden that it used to be.
"There's been a lot thrust on my shoulders at a very young age," she says. "I -- thank God. I don't know how I could have handled it, but I have and I'm still here. And that's -- that's saying a lot, you know?"