In February 2016, the couple welcomed their first son Rocco Robin Cannavale and then a year later in November, along came their second Rafa, named after tennis champ Rafael Nadal.
"There was a bit of an adjustment, at first Rocco didn't get having the brother and he would sort of wake up in the morning and go 'No Rafa!' It's quite a trauma on them I think in the first few months but it's good, toughens them up!" she laughed on Live With Kelly and Ryan in 2018.
Rose is also a stepmother to Jake Cannavale, Bobby's eldest child from his marriage to Jenny Lumet, who was born in May 1996.
When asked what it's like bringing up two baby boys, Rose described the experience as "completely bonkers" to Mind Food in 2018.
"You’re always like, ‘Don’t hit him! Put down that thing! It’s on fire! What’s happening?’ It’s completely chaotic and I’m not by any means a completely in control parent. I definitely am trying to put out fires all the time," she said.
"I’m always thinking I’m going to be on top of everything and I never am. I’m always completely overwhelmed. I have no business telling anyone how to do parenting I’m totally learning on the job.
She added: "What’s great is the universal language you have with people, calling mum or my sisters or my best friend or people I work with, anyone, and I’ll ask, 'How did you do this?' That’s what’s really lovely about having a family is the instant kind of community you find."
Rose has also made an effort to raise her boys with a knowledge of gender equality.
“For a start, I teach them [about women’s rights] by being a working parent,” she told Marie Claire Australia.
“We’re an example of a household that balances both parents going out to work. But I also totally respect mothers who stay home. It’s really hard work and recognising that is what Gloria Steinem fought so much for. Why is [raising a family] not working? What goes on in the home is the most beneficial contribution to children and [society].”
Speaking of her husband, Rose added: “I’ve been around a long time, and there’s not a lot of male actors of Bobby’s calibre who are willing to do that [play support to a female lead].
“He’s one of the few fantastic actors who will, so he’s had some incredible parts in great films, where the protagonist happens to be a woman, like Blue Jasmine [starring Cate Blanchett] and Homecoming with Julia Roberts.”
The couple have worked together on numerous occasions in projects including comedy flick Spy, indie comedy Adult Beginners and in play Medea.
“It starts out as a very pragmatic thing,” Bobby told Vanity Fair. “You have the kids, the kids are getting bigger, and you don’t want to spend the time apart.”
Before the global pandemic, Rose and her family were based in Brooklyn, New York but are currently residing in her home country of Australia.
“It’s still quite full-on back in America, so we’re happy to enjoy the safety of being in Australia until at least the beginning of summer,” she said.
“Australia’s always going to be my emotional home. My children were born in America, and I’ve been based there for many years, but I will always have a feeling, a little bit, of being an outsider.
“Australia is where my family and earliest memories and friendships are – all the grounding things in my life are here.”
WATCH BELOW: Rose Byrne reveals how she'll keep her son in touch with being an Aussie
As for how the mum-of-two is keeping her kids in touch with their Aussie roots, it's with a national delicacy.
"Vegemite, a lot of Vegemite! Breakfast lunch and dinner," she said on Sunrise before adding, "It's an acquired taste."