No Hot Vampire Love on the True Blood Set

09/24/2009 AT 03:25 PM EDT


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.

"It doesn't affect their work," he said. "You don't really see it that much."

And, though Sam's changeling character Sam Merlotte pines for Paquin's character Sookie Stackhouse and is jealous of Moyer's vampire Bill Compton on the show, there's only happy wishes for the real-life couple.

"I think they're both just really independent, really talented people, and they just kind of fit together," Trammell says.

"They've been together a long time, and it's working out," he says. "I'm happy for them."
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