The Muse star - who welcomed his first child into the world on July 9 - tweeted a picture of his actress fiancee cuddling their boy, adding the caption "Family life!"
It is the first time Bingham has been seen by the public, and he appears to be sleeping soundly on his mother with his hand to his mouth in the photo.
Kate, Matt and Bingham had arrived at LAX airport in Los Angeles earlier today (15.08.11), bringing their son through the airport wrapped in blankets to avoid waiting paparazzi.
Kate - who also has son Ryder, seven, from her marriage to rocker Chris Robinson -recently admitted she has been relying on her mother, Goldie Hawn, for advice on how to juggle her career and being a mother.
She said: "We've definitely had lots of talks about parenting and being a working mom.
"My parents allowed my brother and I to have our freedom and be ourselves and feel confident in our choices and to make mistakes without too much judgment. I hope that I can do as good a job."
The 'Something Borrowed' actress also admitted she and Muse singer Matt are in no hurry to get married.
She said: "One thing at a time. We'll say hello to our new one and enjoy that for a while."