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Miller, who had a roller-coaster relationship with Jude Law and broke up with actor Rhys Ifans only weeks ago, has been quietly dating Getty for "at least two months," said a source.
Miller, sporting a sailor's cap, was also spotted topless on the balcony of an Italian hotel room kissing Getty. Meanwhile, the Brothers & Sisters actor, 33, and his wife Rosetta "have been living separate lives for a while," a source tells PEOPLE.
Getty, who has a tattoo of his wife's name on his chest, married Rosetta in May 2000. They had their fourth child together 10 months ago.
"It's humiliating," a friend tells PEOPLE. "Rosetta left the country to protect the kids, and he continues to see Sienna publicly."
The two met through Getty's Brothers & Sisters costar Matthew Rhys. Rhys, who briefly hooked up with Miller, was livid when the photos of the couple surfaced, says a source.
For more on Sienna and Balthazar's romance, pick up this week's issue of PEOPLE, on newsstands Friday.
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
Note that this week’s cover of PEOPLE may differ regionally
