A source told E! News that the new parents are over the moon about their twins.
"Everything is going great with the babies. [George and Amal] are happier than they have ever been and really enjoying being parents," the source said. "They are truly in love and just want to be with the babies and not do much else."
For a while, that seems to be what they plan on doing.
"Amal is not working, and they both have the summer off and are enjoying Lake Como," the source said. "They are very happy to be in Italy."
The source added, "Amal's mother helps out a lot and can't get enough [of the babies.] If she doesn't see them for a few days, she is dying to come back."
In Italy, E! said the couple has a baby nurse who assists them at night.
The nurse helps "with feedings and teaching them about newborns and schedules. Especially with twins, there is a lot of structure and planning to be done and they are grateful for the help," the report said.
A seemingly endless stream of friends are also dying to be around the babies and the new parents.
"They have had a lot of friends visit and Amal's family is often around," the source said. "There is always someone who can give a helping hand. That's given George and Amal an opportunity to be together and have some one-on-one time, too."
After the birth, George's father, journalist Nick Clooney, told the FOX affiliate in Cincinnati that after speaking with the new parents via video chat shortly after the birth, George's mom, Nina, "swears [the twins] have George's nose." Nick also revealed that both children have dark hair.
Following the birth of the twins, Amal's mother, Baria Alamuddin, told People magazine that George and Amal were made to be parents.
"Oh my God, they were so beautiful, so happy, so contented," she said. "You just look at them and you feel like they've been a mother and father for their whole lives."