The Last Week Tonight with John Oliver host and his wife Kate Norley are the proud parents of a second son born about three months ago, he told PEOPLE exclusively Monday night at the 2018 Emmy Awards Governors Ball.

“I have no idea! We have a 3-month-old, so as far away from the 3-month-old as possible,” Oliver, 41, joked of where he’d be displaying the trophy he nabbed for outstanding variety talk series, for the third year running.

The show also took home the awards this year for outstanding writing for a variety series and outstanding interactive program.

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The new dad — who also shares a 2½-year-old son with Norley, an Iraq war veteran whom he met at the 2008 Republican National Convention and married in 2011 — admitted he was “tired,” but that having two children has been “the best” experience nevertheless.

“It’s bewildering [and] exhausting juggling that and the show, but no, it’s the greatest,” Oliver explained.

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The English funnyman joked that his new son “doesn’t do anything” of note at the moment aside from “sleeping, s—ing and crying, in perfect rotation,” but shared that his older child is hitting a big milestone.

“He’s going to start preschool. It’s going to be incredible,” Oliver said, adding of his own potential waterworks over his first child heading off to school, “As a British person, I don’t really have a middle ground — it’s either no emotion at all or I’m collapsing in tears.”

“So it will probably be the second one,” he quipped.