Carey has launched DemBabies.com, which is part of her official website, to keep fans up-to-date on Moroccan and Monroe's development and it includes some adorable photos.
A message on the website reads, "We deliberated for so long about how to reveal the first pictures of our babies to the world. We just didn't want to do the typical thing and display them in a tabloid (not that there's anything wrong with that).
"We decided to share this beautiful experience with you in a special intimate portrait of our family. Parenthood is absolutely the most life changing experience we could ever have imagined. The love we feel for these babies is above and beyond anything we'd ever dreamed of."
Photographs in the online album include Carey holding one of the babies in hospital, swimming with daughter Monroe, and the family-of-four dressed up as superheroes 'The Incredibles' (above).