“It was special to see George wearing the blue hospital gown similar to the one he wore in ER,” Baria, who was on hand for the June 6 birth of twins Ella and Alexander, tells PEOPLE in the magazine’s new issue.
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In the months leading up to the delivery, George himself referenced his ER training grounds.
Asked in March how he’d fare with two kids, the star deadpanned to E! News, “I played a pediatrician on ER, so I know how to work on extra children … If there’s any accidents, I’m there. I’m the guy.”
True to form, George also brought his signature good-natured personality to the delivery room. “He’s always joking, always smiling — his spirits are just unbelievable,” Baria says.
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That smile was on full display after Ella and Alexander were born, she adds. “They were so happy, so contented,” Baria shares of the new parents. “You just look at them and you feel they’ve been a mother and father for their whole lives.”
For more on George and Amal Clooney and their new life with the twins, pick up the latest issue of PEOPLE, on newsstands Friday.