“My husband has a really, really beautiful relationship with Harry," the American Idol and Smash star told Access Hollywood.
"They’re so cute, they’re like father and son,” Katharine revealed.
“We just stay in touch with them. Meghan and I knew each other from childhood, but really, Harry and my husband are friends, and it’s really nice."
The singer, who grew up in LA, just like Meghan, actually went to the same high school as the Duchess of Sussex.
"She went to a school called Immaculate Heart, as did I. She went there for middle school and high school, and I went there just for middle school,” Katharine revealed.
"I did a couple shows with her and she was always put together and great. I was never really close friends with her,” she explained.
Since they have both found fame and fortune, Katharine revealed she and Meghan have caught up a few times in public together.
“But when I was in London doing [theatre production] Waitress, we went to a big charity event … me and David put ourselves in the position where we could at least say hello, and they were really gracious," she said.
On March 31, Harry and Meghan formally stepped back as senior working members of the royal family as they sought to be financially independent from The Firm.
They are no longer referred to as “His and Her Royal Highness” and are forbidden from using the word “royal” to promote themselves, resulting in the dissolution of their brand Sussex Royal.
The couple are currently living in a rented house in LA that once belonged to US star Tyler Perry.
Harry's father Prince Charles is currently isolating in the UK amid strict lockdown rules and tested positive for COVID-19 in March.