During an appearance on The Ellen DeGeneres Show, the singer said that she and Cibrian always try to keep things in perspective and have a good sense of humour in the face of negativity.
Rimes explained: "You have to really take the high road a lot of the time when you want to stand on a mountain and scream like, Why are you saying this?
"We've always put his kids first. We took the kids into consideration with everything that we do. Sometimes you just want to scream. But you don't. We've learned to let it go and laugh at it at the end of the day."
Rimes also addressed repeated rumours that she suffers from an eating disorder which has made her painfully thin, saying: "[The media is] very irresponsible calling a lot of people fat or anorexic or bulimic or whatever it may be.
"It seems like bullying now instead of really taking these diseases seriously that a lot of people are going through."
Rimes, who married Cibrian in April 2011, has previously described love as her greatest accomplishment.
Playboy Club actor Cibrian recently spoke out against the rumours over Rimes' weight, admitting that it bothers him to hear the accusations as his wife is completely healthy.