No Hot Vampire Love on the True Blood Set

Sam Trammell

John P. Johnson/HBO

09/24/2009 AT 3:25 PM ET

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They may be all over each other off-duty, but when True Blood couple Stephen Moyer and Anna Paquin are together on set, they’re as smooth and cool as, well, vampires, according to costar Sam Trammell.

“They’re so professional, I had no idea they were together at first,” he said at the PEOPLE/Entertainment Tonight Emmys after-party on Sunday night. “And then I had no idea he’d proposed to her.”

Even now that the cat’s out of the bag, Trammell says, you’d be hard-pressed to figure out their onscreen chemistry continues off-screen as well.

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