The couple announced the pregnancy in April.
Paquin's expanding baby bump apparently caused problems for the show's writers because they were trying to conceal her pregnancy.
Creator Alan Ball explained: "So, in the last few episodes, Sookie's holding a big purse in front of her at all times.
"I actually heard from the costume designer about midway through the season, she went, 'Sookie can't wear a Merlotte's [restaurant] T-shirt anymore.'
"And I went, 'Well, it's a good thing Sookie isn't really at Merlotte's anymore, she's basically trying to save the world.'
"So, we'll put her in loose-fitting, save the world outfits."
Moyer, who has children Billy, 12 and Lilac, 10 from previous relationships, recently joked Paquin being pregnant brings the "crazy" to his already extended family.
He said: "I love my kids so much. And I think the fact that Anna is pregnant just adds more crazy to the bundle of fun."
Season five of True Blood began recently on Prime on Thursday nights.
- Herald online with Bang! Showbiz