The yoga instructor recently uploaded a tender snapshot of her and little Carmen lying side by side. The mother and her two-week-old daughter look the picture of happiness as Hilaria affectionately watches over her sleeping baby and cradles Carmen close to her chest.
"Our beautiful little Carmen. Photo by the talented @CKnightPhoto," tweeted Hilaria alongside the photo.
The new mother uploaded another close-up of Alec catching up on some much-needed rest, next to his baby daughter who is serenely fast asleep beside him.
"Carmen likes to take a siesta with her daddy," wrote Hilaria next to the image.
The beautiful couple introduced their newborn daughter to the world in an exclusive interview with HELLO! following the baby's birth on 23 August.
"From 7am to 7pm she's a great sleeper," Alec told HELLO! "Then at night she says, 'Let's have a conference.'"
But the proud new parents are more than happy to forgo sleep. "Last night we were sitting there, and you realise, I'm not going to have this moment again. I just want to enjoy every moment," said Alec.
"We have trouble sleeping because you just want to stare at her," Carmen's besotted mum added.
Alex is already father to 17-year-old model Ireland Baldwin from his previous marriage to actress Kim Basinger.