After inviting her to come out for her interview, Alec jokingly shakes his wife's hand before leaning in to give her a hug and a kiss on the cheek.
"Do you guys know that he shook my hand and didn't kiss me for six weeks when we first met?" Hilaria reveals immediately after the applause dies down.
"You shouldn't tell them that!" Alec exclaims in response.
Hilaria goes on to reveal that, while in the early days of their relationship, Alec would tell her "all these things, like, 'I'm gonna marry you. I'm gonna spend the rest of my life with you. We're gonna have a ton of kids.'"
"And then he would shake my hand at the end of the night," she says.
"I didn't want you to think that I just wanted to have sex with you!" Alec explains.
The couple continues their appearance by doing an audience Q&A, which largely focuses on their four children, Carmen, 6, Rafael, 4, Leonardo, 3, and Romeo, 1. Alec also has a 24-year-old daughter, Ireland, from a previous relationship.
"It works well. I'm a very type-A personality and I need to be the boss. So he goes off and he doesn't bother me too much while I parent," Hilaria says of raising kids with Alec, before revealing one of the challenges they face.
"He'll do the typical dad stuff that drives me crazy. Like, I'll have the kids ready for bed and he'll go in there and be like, 'Let's wrestle!' And then he leaves and he's like, 'Enjoy putting them to bed,'" she says.
Hilaria also shares how they work to maintain their thriving relationship amid their busy day-to-day life.
"He said to me when we had our first [child], 'Not only are you going to be my wife and the mother of our child, but you're my girlfriend. You're always gonna be my girlfriend,'" Hilaria recalls. "And so we relate to each other like that [with] our banter. We're always flirting."
"In terms of timing, you just gotta find time! You have to make it a priority because people have needs," she adds.
Prior to Hilaria's sit-down with Alec, the Saturday Night Live actor opens the show with a hilarious monologue, in which he pokes fun at his connection to Justin Bieber, who's married to his niece, Hailey Bieber.
"I've been in show business a long time and I've done a lot of great things. I have an Oscar nomination. I won seven SAG Awards for 30 Rock -- that's actually the record for most SAG Awards by any other actor. I have a star on the Hollywood Walk of Fame," he says. "But of course my greatest achievement is, I'm Justin Bieber's uncle."
"My niece is married to the Biebs. And I just want to say to you all up front, no, I can't get you concert tickets," he continues. "I don't know Justin that well, but I know Justin's friends with Ellen, so he's probably watching. So Justin, if you're out there, congratulations on your new album and please follow me on Instagram."
Watch the video below for more on the Baldwin family.