The couple are "absolutely not" getting married in June, Madden told PEOPLE Thursday at the Pampers "Dads on Diaper Duty" party in Manhattan. "We haven't even started planning," the rocker said.
Madden, 31 noted that he will be out on tour in the U.S. and Europe through most of the summer. But he and Richie, 28, are not in a rush to wed. Instead, they are concentrating on raising their family.
Son Sparrow, 9 months, is "becoming a little person," who is on the verge of talking, says Madden. "He's really easy, just like Harlow. They're the easiest kids."
These days, Harlow, 2, loves to point out all the things she can do that her younger brother can't yet, including running, climbing stairs and eating with a fork. Still, the two kids are the best of friends, and Madden credits their good behavior to Richie's great parenting skills. "She's supermom," he says.
But being a parent hasn't taken away Richie's devious side: "Nicole always hacks my Twitter and writes the weirdest things," Madden says with a laugh. "It's embarrassing, really."
Still, her playfulness is one of the qualities Madden loves about Richie. "She has a very sick sense of humor," he says. "Motherhood has not taken that away."