"I just spent the last weekend – Mom was rehearsing for Chicago – being Dad without a nanny, without Mom, and didn’t burn the house down," the Fall Out Boy bassist, 30, told PEOPLE on Tuesday at the American Eagle Outfitters Times Square store opening. "So I’m pretty excited about that."
The couple's son, Bronx Mowgli, turns 1 on Friday, and will get to enjoy the company of both parents and friends at a SpongeBob SquarePants-themed birthday party in Los Angeles.
"He likes Bob and he likes guitar – which he calls 'itar,’ so we're going to have a Spongebob party for him," Wentz said.
On the guest list? "A bunch of friends," he said. "Like all the guys in Blink  and a couple friends that have kids [are coming over]."
Simpson-Wentz, 25, makes her Broadway debut as Roxie Hart Nov. 30. (She played the role in the London production in 2006.)
Bronx may need a babysitter that night. Asked if he will be attending his wife's debut, Wentz said, "I think I will be."