He and Richie have two young children together.
"I keep getting e-mails from old friends and family asking about a wedding," Madden, 30, wrote Wednesday on the Web site of his band Good Charlotte. "NO we didn't get married."
Richie, the 28-year-old daughter of singer Lionel Richie, is a former reality television personality.
Celebrity Families of 2014 [PHOTOS]