Olivia Munn and John Mulaney Are in ‘Total Bliss’ After Welcoming Baby Daughter Méi June: Source (Exclusive)

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

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

One day after the happy news was shared on Instagram, a source close to the couple exclusively tells PEOPLE, “They are in total bliss with Méi and Malcolm,” referring to the couple’s 2-year-old son.

“After everything they have been through there’s no tighter, closer little family,” the insider adds.

Mulaney, 42, and Munn’s new addition joins their son Malcolm 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.

In April, Munn, 44, 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. She said calculating her lifetime breast cancer risk score using a free online tool called a Tyrer-Cuzick risk assessment calculator “saved my life.”

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.

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

Munn first shared the happy news about baby Méi with an Instagram announcement featuring a photo of herself sitting on Mulaney’s lap as she held their daughter in a hospital room.

“Méi June Mulaney came into the world September 14, 2024, the year of the dragon🐉.”

“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💜.”

Mulaney also shared the news on his Instagram. 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.”