Rimes was featured on the cover of Us Weekly with the headline "Caught in an Affair."
The magazine shows a photo allegedly taken from security video at two Laguna Beach establishments, which reportedly show the pair holding hands and kissing.
Us Weekly reports Rimes, 26, and Cibrian, 35, met on the set of TV movie "Northern Lights."
Rimes is married former backup dancer Dean Sheremet when she was 19 and some tabloids point to the fact that she married so young as the reason for straying.
Cibrian is married to model Brandi Glanville and the pair has two children.
In response to the magazine reports Rimes posted a message on her official Web site saying:
This is a difficult time for me and my loved ones, but I appreciate all your continued support.
I would like to assure all of you that this is a place for you to hear things directly from me and as you all know, not everything in our lives is always black and white.
Meanwhile her husband is taking to Twitter to battle the rumors simply saying "I love my wife!!" Perez Hilton verified it is indeed Sheremet's Twitter account.
What the El!?! Editorial:
Wow, you never want a tabloid to get security camera pics of you and your TOTALLY HUNKY co-star kissing at dinner!
I have a feeling we're going to hear divorce news in this one. Wonder how Mrs. Cibrian is feeling. I'm guess not good.