Benji Madden "feels so lucky" to have wife Cameron Diaz and daughter Raddix

He wrote: "My Wife and Daughter fill me up with so much gratitude. Everyday, I feel so lucky. Just wanted to say it out loud!!! Much Love & Best Wishes."

Cameron and Benji previously shared their baby news in a joint statement, in which they said they were "so happy, blessed and grateful" to have added to their family.

The statement read: "Happy New Year from the Maddens! We are so happy, blessed and grateful to begin this new decade by announcing the birth of our daughter, Raddix. She has instantly captured our hearts and completed our family ... While we are overjoyed to share this news, we also feel a strong instinct to protect our little one's privacy. So we won't be posting pictures or sharing any more details, other than the fact that she is really really cute!! Some would even say RAD:) From our family to all of yours, we're sending our love and best wishes for a Happy New Year and Happy New Decade ... Sincerely, Cameron & Benji (sic)"

And the pair have been "in BABY bliss" ever since.

A source previously told PEOPLE: "They waited for so long to have a baby, so now they are just enjoying their daughter. They are still in baby bliss and the happiest parents. They take turns staying with the baby and don't really leave the house together. They spend time with their families, and close friends at home but don't take their daughter out. They are very protective of her and careful because of the flu season. Cameron always imagined what motherhood would be like. You can tell that it's so much more than she ever imagined. She really is the happiest ever. Spending the past couple of weeks with her daughter has been magical for her."