"I love it," the actor told PEOPLE Monday at the premiere of HBO's The Normal Heart in Los Angeles. "It's the most profound gift and the most daunting challenge at times."
Bomer, 36, has three sons with his publicist husband, Simon Halls. The eldest turns 9 this weekend, and they also have 6-year-old twins. Bomer recognizes the huge responsibility that comes with parenting, and says it's a balancing act.
"I just want to be hopefully somebody who helps shape these souls without changing how they came into the world," he says. "To just give them the structure they need to thrive in the world but at the same time let their own personalities shine through. Some days that's easier than others."
Known for his work on the USA drama White Collar and in films like Magic Mike, Bomer is winning early raves for his role as Felix Turner in The Normal Heart, based on Larry Kramer's Tony-winning play about the AIDS crisis.
He lost more than 35 lbs. for the movie. And he does want his children to see it – eventually.
"They're really young. So, not anytime soon," he says. "It's definitely a film I want them to see at a different point for a lot of reasons. This project is bigger than me. It's something I want to show them to understand a piece of my history. And who they owe a lot of thanks to."
He adds: "I hope people see this movie and respond the way I did when I was a teenager, with a sense of gratitude for this generation who stood up when it wasn't popular and it wasn't easy to do so … They are the reason I'm able to get married today, and probably the reason I can walk down the red carpet with my husband."
Saying he is "grateful for so much in my life right now," Bomer is looking forward to spending the summer in New York with Halls and the kids while he films the next season of White Collar.
"I need a summer with the family," he says. "One of our twins has lost both of his front teeth. I was so happy yet so sad because it totally changes the way he looks! He's so cute right now because he's got this little empty space there. It's really fun."
Reporting by MATTHEW COLE WEISS