He scores big laughs on his late-night talk show, but when Jimmy Kimmel comes home, he’s faced with a tough crowd: his two young kids. “I keep telling them I’m this big, funny TV star, and they don’t seem to care,” Jimmy, 51, exclusively told Closer Weekly in the magazine’s latest issue, on newsstands now, of daughter Jane, 5, and son Billy, 2, at the recent LA Loves Alex’s Lemonade culinary event.

“If I see a billboard with my face on it, I’ll pull over and make them get up on the roof of the car so they can appreciate it, but they don’t,” he jokes. Part of the problem, Jimmy says, is “they think everybody’s father is on TV. I don’t think they know the difference between a TV and an iPhone.”

Jimmy Kimmel Family

More important, Billy, who was born with a congenital heart defect, is “doing great,” Jimmy says. “He thinks he’s Spider-Man. He wears the costume all the time and shoots webs all over the house. So we’re safe from crime.”

This past April, Billy turned 2 years old and Jimmy celebrated his kid’s special day by thanking the doctors who saved his son’s life. “Happy 2nd birthday to our little #Easter buddy Billy,” the comedian wrote via Instagram. “We are grateful always to the nurses and doctors at @CedarsSinai & @ChildrensLA who saved his life and all of you who prayed and sent positive thoughts our way.”

Billy’s son has already undergone multiple open-heart surgeries, and when he gets older he’ll have to get a few more procedures to make sure he’s in tip-top shape. “He’ll have another surgery when he’s around 6 or 7 years old, but in the meantime, he’s doing great,” Jimmy previously revealed to Oprah Winfrey.

The comedian’s friend Ellen DeGeneres also did something very sweet for Billy that he’ll cherish forever. “We called our friends at Children’s Hospital LA,” she said during her talk show. “We have named one of the rooms of the Heart Institute floor in honor of Billy. That will forever be the Billy Kimmel room.”

What an amazing gift!

For more on Jimmy Kimmel, pick up the latest issue of Closer Weekly, on newsstands now — and be sure to sign up for our newsletter for more exclusive news!