John Oliver plans to display his brand-new Emmy "as far away from the 3-month-old as possible," he joked to PEOPLE Monday night following his big win

Emmy Winner John Oliver Reveals He and Wife Kate Welcomed Their Second Child Three Months Ago

John Oliver has his shiny new Emmy in one arm — and a new baby in the other!

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.

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“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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Image zoom John Oliver Kevin Winter/Getty

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.

Image zoom Kate Norley and John Oliver Dan Steinberg/Invision/AP

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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.”