And a more than a little relieved. Chernukha admits the pregnancy was made difficult for her daughter, 39, a pianist and composer, by the intense interest of the media. "I'm very pleased for her because during her pregnancy she worried a lot because of all the bad press written about her. Lots and lots of lies," she says.
Grigorieva's pregnancy was announced six weeks after Gibson's wife of 30 years, Robyn Moore, then 53, filed for divorce last April. Gibson, 53, and Moore have seven children together.
"Her pregnancy was a hard one even though she had no [medical] problems with it," says Chernukha. "And, of course, Mel supported her and so did all her friends." Grigorieva – who also has a son, Alexander, 12, fathered by James Bond actor Timothy Dalton – tries to stay above the headlines, says her mother. "She doesn't make any statements or get involved with refuting what's said about her. She just tries to keep herself closed off from all the journalists."
Chernukha says she has spoken to her daughter since the birth and notes that the baby was two weeks early. (A friend of the couple tells PEOPLE that mother and child are both fine.)
The grandmother hopes her daughter and child will visit soon – and she may get her wish. While promoting her new album, Beautiful Heartache, in the U.K. earlier this year, Grigorieva told reporters of her plans to take Gibson and the baby back to her homeland next year. "Russians are very nostalgic," she said.