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The couple has welcomed twins, with Greenberg, 43, announcing the happy news on Sunday via Instagram. "We got double the trouble now @jamiejchung 👶🏻👶🏻," he captioned a video of himself snuggling the two infants on his chest.
The Lovecraft Country star, 37, commented on her husband's post with two heart emojis. Chung also shared the adorable video to her Instagram Story.
The pair, who tied the knot in 2015, are also parents to a fur baby: their miniature Schnauzer-Shih Tzu named Ewok.
"It's always nice, especially with a partner, to be able to put something else before ourselves, and it's taught us a lot of responsibilities," Chung told PEOPLE in 2017. "It's kind of like a training baby, I guess you could say. It's wonderful. It requires us to communicate more with each other."
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In 2019, the actress opened up to her Instagram followers about freezing her eggs.
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"Here I am over a week ago at my doctors office getting an orientation/lesson on how to inject myself with growth hormones. One of the first major steps for egg retrieval," Chung captioned a photo of herself at the time, holding up an instruction sheet titled "EMBRYO CREATION" in front of her face.
The Real World alum revealed she had "been stewing" over the idea of freezing her eggs for two years, and recently decided to get the process started.
"I did my research on facilities and then it all boiled down to these deciding factors; I want options. I'm buying time. I'm unsure and scared and hopeful," Chung continued, adding of husband Greenberg, "I have the best life partner a person can ask for and I know I want to one day raise a child with Bryan. I'm just unsure when that will happen. And I realized that's ok."
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"A lot of people have told me that 'There is no right time. Just do it! What are you waiting for?! It's the best thing to have ever happened to us!!' And I believe it all but I'm going at the pace that's right for me because I'm not ready just yet," she wrote.