Olivia Munn, John Mulaney in ‘Total Bliss’ after welcoming baby Méi: Source (exclusive)

Olivia Munn and John Mulaney couldn't be happier as a family of four.

On Sunday, September 22, the couple announced that they had welcomed their second child, a daughter named Méi June, via surrogate on Saturday, September 14.

A day after the happy news was shared on Instagram, a source close to the couple told PEOPLE exclusively: “They are totally happy with Méi and Malcolm,” referring to the couple's two-year-old son.

“After everything they've been through, there's no closer, more intimate little family,” the insider adds.

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Mulaney, 42, and Munn's new addition is their son, Malcolm, whom they welcomed on Nov. 24, 2021. Their announcement comes just months after they tied the knot in an intimate ceremony at a friend's home in upstate New York in July.

In April, Munn, 44, opened up to PEOPLE about her “horrific” breast cancer diagnosis a year earlier, which led to four surgeries, a bilateral mastectomy and medically induced menopause. She said calculating her lifetime risk of breast cancer using a free online tool called the Tyrer-Cuzick Risk Assessment Calculator “saved my life.”

Despite her difficult journey since her diagnosis, the actress shared an update on Instagram on September 4 that she is “doing well,” posting a video with a detailed timeline of her cancer journey, including undergoing a “nipple retraction, lymph node dissection, and bilateral mastectomy” in May 2023 after receiving the diagnosis the month before. She underwent an egg retrieval in June 2023 and breast reconstruction in September 2023.

The actress also underwent a partial hysterectomy/oophorectomy in April 2024.

Munn first shared the happy news about baby Méi in an Instagram post that included a photo of her sitting on Mulaney's lap in a hospital room, holding their daughter.

“Méi June Mulaney was born on September 14, 2024, the year of the dragon🐉.”

“I had so many deep emotions about not being able to carry my daughter. When I first met our surrogate, we spoke mother to mother. She showed me so much kindness and understanding that I knew I had found a true angel,” she continued. “Words cannot express my gratitude for protecting our baby for nine months and making our dreams come true.”

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

Mulaney also shared the news on his Instagram. The new father of two wrote: “Méi June Mulaney was born September 14th, 2024, the year of the dragon🐉. We stole so much stuff from the hospital,” he joked, adding: “I love my little girl so much.”