Debra Messing and Will Chase
01/27/2012 AT 11:00 AM EST
Looks like Debra Messing's Smash
romance is getting serious!
The star of NBC's upcoming musical series (premiering Feb. 6, 10 p.m. ET) and her on-and-offscreen love interest, Will Chase
, attended the N.Y.C. premiere for the show Thursday night, and hit a major relationship milestone in the process.
At an opulent dinner after the premiere, Chase, 41, met Messing's parents, sidling up to her father in a booth while the actress's mother sat on his other side.
A show insider confirmed to PEOPLE last month that the costars were dating
– shortly after Messing, 43, confirmed that she and her husband of 10 years, Daniel Zelman, separated
in 2011. (Chase also recently split from his wife.)
After the Cinema Society premiere, sponsored by Volvo, dinner was served steps from the striking Temple of Dendur at the Metropolitan Museum of Art. Guests dined on towers of lobster, shrimp and lamb chops at low, dark banquettes, and after eating, the couple laughed and talked while sandwiched between Messing's parents.
"We all get along famously," Messing told PEOPLE of the close-knit cast. Asked if she was happy, the actress smiled broadly and provided a telling one-word answer: "Very."
The costars' off-screen relationship isn't exactly surprising, director Michael Mayer tells PEOPLE. On-set romances are common behind the scenes on Broadway, the subject of Smash
, he says. "On Broadway, we call it a 'showmance,' " says Mayer. "That’s where people meet and fall in love."
"I don't know where Debra and Will would have met [otherwise], says Mayer. "So [Smash
] brought them together. And the context of their onscreen relationship, I'm sure that triggered a lot."