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FIRST PHOTOS: Nicole Richie and Joel Madden Introduce Baby Sparrow!

10/21/2009 at 07:30 AM EDT

FIRST PHOTOS: Nicole Richie and Joel Madden Introduce Baby Sparrow!
Nicole Richie and Sparrow

Joel Madden

Joel Madden

Six weeks after welcoming their first son, Nicole Richie and Joel Madden – along with their 21-month-old daughter Harlow – are showing off the latest addition to their family, Sparrow James Midnight Madden.

"I couldn't be happier," Richie tells PEOPLE. "The only thing you want is for your kids to be healthy and happy, and they are. I'm right where I belong."

In an interview at their home in Laurel Canyon in Los Angeles, Richie, 28, and Madden, 30, her boyfriend and front man of the band Good Charlotte, say they are deprived of sleep, but grateful their daughter Harlow is now fawning over a baby brother.

"I'm glad I had a girl before I had a boy," says Richie. "She just loves him so much." Adds the children's proud papa, "She's very gentle with him."

For much more on Richie and Madden's expanding family – including the decision to name their baby boy Sparrow, how Richie's second pregnancy was different from her first, and how she's losing her baby weight – pick up the latest issue of PEOPLE, on newsstands Friday. (Save a dollar on the new issue. Click here for coupon.)

FIRST PHOTOS: Nicole Richie and Joel Madden Introduce Baby Sparrow!| Babies, Joel Madden, Nicole Richie

Nicole Richie with Sparrow, Joel Madden with Harlow

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