Jolie gave birth to her and Pitt's fifth and sixth children -- a boy and a girl -- Saturday via Caesarean section at the Fondation Lenval Hospital in Nice, France.
People.com quoted Dr. Michel Sussmann as telling reporters outside the hospital that Pitt and Jolie "were talking, they were together" during the delivery.
"It was an epidural, so (Angelina) was awake and speaking and laughing. They were happy," Sussmann reportedly said, adding that Pitt never left his girlfriend's side.
"He was my assistant!" Sussmann quipped, revealing the actor even cut the babies' umbilical cords. "He was ... perfectly calm, totally determined, very pleased to be at the birth of his children, very moved and very emotional."
The obstetrician also said there were "absolutely no problems" during the delivery but he said he wasn't sure when Jolie and the babies would be leaving the hospital.
"She will stay for a few days," he said. "The babies are fine. The babies are with the mother and father and they are fine."