Madden and the reality TV starlet are the parents of an infant daughter named Harlow.
"We don't have any plans for that right now," Madden told People.com Wednesday when asked if he and Richie planned to marry. "We're just happy, and we're being a family, and that's where we're at right now. But marriage means something different to everyone. ... Right now we're really happy and we're concentrating on our family, and that's what is making us happy right now. We're moving at our own pace."
Madden told the entertainment news Web site he is enjoying fatherhood.
"It's crazy," he said. "Every day (Harlow) does something new. When she reaches for me, it's awesome! Just watching her grow, it melts me!"
Madden is the frontman for the rock band Good Charlotte. Richie is best known for co-starring with Paris Hilton on the TV reality series "The Simple Life."
Celebrity Families of 2014 [PHOTOS]