"We had a funny old thing a few seconds ago, didn't we Hilary?" Henry said at the start of the clip.
Barry cuts in, saying Henry told her he could "see breast".
"And I could, but now you've tucked it away nicely so that's good," Henry replied.
Barry joked that anyone listening on radio would be turning to TV - the show is simulcast on both media - then added that the moment had passed.
"It's over. It's over," she said.
However, Henry wouldn't let the subject drop.
"Oh really. That's how much you think of your breasts?," he asked, causing sports presenter Jim Kayes to burst out laughing.
"Paul, you can't say that. You just can't say that," Kayes protested.
Digging his heels in, Henry ploughed on.
"They're gorgeous, I can tell you first hand. I'm constantly distracted when I turn over and look at Hilary there. I'm sorry. I just am.
"How long have they been making blouses? How hard is it to make the buttons actually hold the fabric together? I can't not. I can't not.
"I just look over and there it is poking out at me."
Barry humoured Henry, telling him it was his lucky day, before adding: "If you're getting your thrills from that, you have a sad life."
The video has been viewed more than 60,000 times on Facebook but many people were quick to question how appropriate Henry's comments were.
"If this happened in my workplace, I'd file a complaint," wrote one woman.
"Hilary -- I'm so sorry you're in this position. Just another example of a highly competent woman 'paired' with a not so bright man."
"Why does she have to put up with it! He's a creeeeeeeep," wrote another.
However, the majority of comments praised Barry for being "a good sport", saying they loved the pair's rapport on the breakfast show.
This isn't the first time Henry has copped criticism for making inappropriate comments about women's bodies.
In 2009, when he was a presenter for TVNZ's Breakfast, he made fun of a woman guest in an incident which became known as "moustache-gate".
Henry read viewer comments that Greenpeace worker Stephanie Mills had a moustache. He then added his own comments, while his co-host Alison Mau pleaded with him to stop.
"That was a moustache on a lady," he said. "People can say what they see, it's television isn't it?"
Later in the show, Mau read a letter from a woman who talked about the medical causes behind female facial hair and said she had been reduced to tears by Henry's comments. "Start a group, really," Henry responded.
TVNZ upheld viewer complaints about his comments and he later apologised.
