“Méi June Mulaney came into the world September 14, 2024, the year of the dragon🐉,” Munn captioned an Instagram post featuring a photo of herself sitting on Mulaney’s lap as she held their daughter in a hospital room.

“I had so many profound emotions about not being able to carry my daughter. When I first met our gestational surrogate we spoke mother to mother. She showed me so much grace and understanding, I knew I had found a real-life angel,” she continued. “Words cannot express my gratitude that she kept our baby safe for 9 months and made our dreams come true.”

Munn concluded her post by sharing the meaning behind her daughter’s name. “I am so proud of my little plum, my little dragon for making the journey to be with us. My heart has exploded,” she wrote, before adding “Méi (pronounced may) means plum in Chinese 梅💜.”

John Mulaney (left) and Olivia Munn with baby daughter Méi. Photo: John Mulaney/Instagram

The mom of two rounded out her post with a closeup of baby Méi, a photo of her cradling her daughter as they sat near a large window and a family photo featuring the new family of four looking out at the ocean.

Mulaney shared a post on his Instagram, as well. The new dad of two wrote, “Méi June Mulaney came into the world September 14, 2024, the year of the dragon🐉. We stole so much stuff from the hospital,” he joked, adding, “I love my little girl so much.”

The comedian also noted the correct pronunciation and meaning of his daughter’s name, complete with a purple heart, just like in Munn’s post.

Mulaney shared the photo from the hospital in his carousel, too, but he also added a video of the little one spitting up on his shirt as he burped her.

The couple’s new addition joins their son Malcolm Hiệp Mulaney, 2, who they welcomed on Nov. 24, 2021, while their announcement comes just months after they tied the knot in July in an intimate ceremony at a friend’s home in New York state.

Sam Waterston, Munn’s The Newsroom costar, officiated the ceremony, PEOPLE exclusively confirmed at the time, while Malcolm and a witness were the only guests in attendance.

Just months earlier in April, Munn had opened up to PEOPLE about her “terrifying” breast cancer diagnosis a year earlier, which resulted in four surgeries, a double mastectomy and medically induced menopause.

Despite her challenging journey since her diagnosis, on Sept. 4 the actress shared an update on Instagram that she was “doing ok,” as she posted a video detailing a timeline of her cancer journey, including that she underwent “nipple delay, lymph node dissection and double mastectomy” in May 2023 following her diagnosis the month before, and then had egg retrieval in June 2023 followed by breast reconstruction in September 2023.

Back in May, Munn told Vogue that after her diagnosis she froze her eggs to allow herself and Mulaney the opportunity in the future to expand their family, after having previously frozen her eggs at ages 33 and 39.

Her Sept. 4 timeline also detailed that she underwent lupron treatment in November 2023, a partial hysterectomy/oophorectomy in April 2024 and, most recently, arimidex treatment in August 2024.

Throughout, Munn has remained focused on her son. When speaking to PEOPLE in April, she shared that being with Malcolm during the course of her treatment has given her deep joy.

“When I’m with him, it’s the only time my brain doesn’t think about being sick. I’m just so happy with him,” she said. “And it puts a lot of stuff into perspective. Because if my body changes, I’m still his mom. If I have hot flashes, I’m still his mom. If I lose my hair, I’m still his mom. That’s really what matters the most to me. I get to be here for him.”

Indeed, over the past few years, Mulaney and Munn have delighted in documenting Malcom’s major milestones as they relish in the joys of parenthood.

Their son has had some big accomplishments already, like saying his first words, trying new foods and even learning how to open doors. As the child of two celebrities, he’s also experienced some pretty cool moments, from traveling to beautiful destinations like Colorado’s Red Rocks Park to visiting his dad in New York City on the set of Saturday Night Live.

In April 2023, the X-Men: Apocalypse actress even posted her and Malcom’s travels to join Mulaney for a stretch of Las Vegas shows.

In addition to sharing Malcolm’s highlight reel, Munn has also opened up about the challenges of raising a child, how she’s adjusting to motherhood and her postpartum journey.

Mulaney has also vocalized his excitement over being a new dad. During a June 2022 appearance on Late Night with Seth Meyers, he opened up about getting to celebrate Father’s Day with his son for the first time.

“He got me a plethora of gifts,” Mulaney said. “I woke up, and I had breakfast with him. And his new thing is when I turn the phone on and it’s in selfie mode and I put it on video, he grabs it and slowly brings the camera into his mouth. So, all his films have the same twist ending.”

More recently, Malcolm helped his mom celebrate her 44th birthday in July, with the actress sharing a sweet video on Instagram that showed the little boy telling her “Happy birthday Mommy!” and that he loved her.

In August, Munn also revealed that Malcom and Mulaney have a sweetly similar trait, when she posted an adorable video on her Instagram showing the father-son duo fiddling their fingers in the same way while sitting together on a couch.

“It’s the exact same fidget. I can’t. 🤓,” she captioned the video.