The 31-year-old Madden fronts the band Good Charlotte.
The couple, who dated for more than four years, have a 2-year-old daughter, Harlow Winter Kate, and a 15-month-old son, Sparrow Midnight.
Richie won national attention costarring on TV's "The Simple Life" with Paris Hilton and has since been a staple in the tabloids. She has recently taken to writing books and designing clothes.
Richie has her own fashion line, Winter Kate, and a shoe and accessories line, House of Harlow.