Meghan Markle is getting candid about family life on a new episode of The Drew Barrymore Show. 

In a preview of the Duchess of Sussex's appearance on the talk show airing Thursday, Barrymore quizzes Meghan with the "fast five," including a question about what her children, Prince Archie and Princess Lilibet, have picked up from their dad, Prince Harry.

Barrymore asks, "What's your favorite thing that you see in your kids that you go, ‘Oh, that's their dad' ?"

Meghan replies, "Oh, some of the words that they still say with a British accent. So they'll say, 'Zebra,' and what else do they say? They have these little moments where it comes out. They have very American accents, but they say words that are just like him, and I think it's adorable. Zebra is a good one."

The Duke and Duchess of Sussex welcomed their son Archie, now 5, when they were still living in the U.K. They relocated to California in 2020, where Lili, now 3, was born.

Meghan recently traveled to New York City to promote her new Netflix show, With Love, Meghan, and her lifestyle brand, As ever. But her husband and kids made sure she could feel the love from across the country, and Meghan took to her Instagram story on Monday to share the bouquet of flowers and handwritten note from her family.

“I felt so loved,” she tells Barrymore on the show. “That [Harry] had planned it in advance to make sure it was there when I got to my hotel room, it was really sweet.”

Meghan also shares how she makes time for her kids when she’s away. 

“I always make it a point when I'm traveling, if I can't do bedtime stories with my kids… I'll always pack a really thin book and I'll videotape myself reading it,” she explains. “So whoever's with them or Papa can say, ‘Here's Mama reading your bedtime story.’”

"You find ways to show up for each other and if that's the one thing that I can convey through the show or through As ever as a brand, I want people to know you can show up for each other because you know how good it feels when someone shows up for you,” she adds.

When it comes to how her relationship with "H," as Meghan calls her husband, has progressed since their first date in 2016, Meghan says, "life is full of surprises."

“I did not expect to meet H, and for this to be our love story and, you know, I'm very lucky,” she shares. “I am married to the funniest, sweetest, most charming [man]...He's an amazing father. And so, you know, I count my blessings because I have him and also I have a partner who is so supportive of me.”

One way the couple keep the love, Meghan shares, is by following some marital advice that she got years ago while working as a nanny in college. 

“One of the dads said to me, he's like, ‘You know, Meghan, when you meet your person one day, I want him to say to you the same thing that I said to my wife when we got married, which is, I vowed to always date my wife.’”

“I told H that when we started dating, he goes, ‘I vow to always date you,’ ” she continues. “So we have this connection, I think, because we're so committed to treating each other the same way you did before you had a ring on it, before it was locked down, when you're just courting each other. You can see all the good and joy in that butterfly period. That's I think what keeps things really alive.”

In an intimate interview with PEOPLE in this week's exclusive cover story, Meghan explains how she's back in a "honeymoon period" with Prince Harry.

“My husband met me when I had The Tig, and I see this spark in his eye when he sees me doing the thing that I was doing when he first met me,” she says.

“It’s almost like a honeymoon period again,” she adds, “because it’s exactly how it was in the beginning when he’d watch me scribbling away, writing newsletters, fine-tuning edits and just really being in the details of it. I think he loves watching as much as I love doing that creative process. It’s just been fun. This is who I’ve always been.”