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"Both Jill and the baby are healthy and the family is thrilled," says her rep. No other details were immediately available.
Gianni joins big brother Marco, who is 4.
The former Law & Order actress, 39, confirmed the pregnancy to PEOPLE in August, when she also admitted she was struggling to find a name that went well with Mastropietro.
"Maybe something Irish," she said.
Hennessy was still at a loss two months later. "If you have anything that rhymes with the last name, let me know," she said.
Besides being an actress, Hennessy is also a musician and has been working on a CD this year.
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
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