The pair began a relationship in 2009 behind the backs of their respective spouses Dean Sheremet and Brandi Glanville, a decision which Rimes has since confessed that she understands was wrong.
"I know I didn't do it the right way," she said in her new special Backstory: LeAnn Rimes. "I didn't have the tools to know how to do it the right way, how to let go the right way. I'd never been taught that."
"I have the strength [now] but I didn't at the time... So, it got really messy, but I have learned a lot from that. And I'm not glad it happened, but I know why it did."
Rimes divorced from Sheremet in June 2010 while Cibrian split from former wife Glanville in August 2009.
Rimes and Cibrian announced their engagement in December 2010.
Backstory: LeAnn Rimes airs Sunday on the Great American Country network.