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The Good Charlotte singer said he and Richie are content "moving at our own pace".
He told People: "We don't have any plans for [marriage] right now.
"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.
"We're concentrating on our family, and that's what is making us happy right now."
When asked how he was enjoying fatherhood, Madden commented: "It's crazy. Every day she does something new.
"When she reaches for me, it's awesome! Just watching her grow, it melts me!"
Richie and Madden had a baby girl, Harlow Winter Kate, in January.
