"From 7am to 7pm she's great sleeper," Alec told HELLO! in an exclusive interview to introduce his little girl. "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," he said.
CLICK ON PHOTOS FOR GALLERY
"We have trouble sleeping because you just want to stare at her," her besotted mum added.
In beautiful family pictures featured in HELLO!, issue number 1294, Alec, 55, and yoga instructor Hilaria, 29, can been seen cradling and cooing over their beautiful baby girl, who lies serenely in her parents' arms.
Carmen is Alec's second child – he is also a father to 17-year-old Ireland from his marriage to Kim Basinger. New to baby bliss is yoga instructor turned Extra correspondent Hilaria, 29.
The happy couple announced their pregnancy news in February, eight months after they were married in a romantic New York ceremony held at St Patrick's Old Cathedral on 30 June.
They tied the knot in front of 175 loved one before moving to the Kimmel Center at New York University, where Alec studied, to celebrate.
"It was the best party I've ever been to," the bride exclusively told HELLO!. "Everyone is saying, 'Can you guys get married again, please?'"
To see the first pictures of Alec and Hilaria’s newborn daughter and read the exclusive interview, pick up a copy of HELLO! magazine out Monday 9th September.