The couple's son and daughter, Charlie and Poppy, were born several weeks early last summer (12) and the tots spent a long time in hospital before their parents were allowed to take them home.
Moyer has now spoken out about the difficult experience, revealing the stress took a toll on the new parents.
He tells People.com, "They had a tough start. They were early and it was touch and go there for a while... It does consume your every thought, and sometimes you cope with it really well and sometimes you don't. Sometimes you're desperately terrified and other (times) you're so tired you can't think of anything, so you just get through it like everybody does."
Moyer also admits the True Blood co-stars celebrate the babies' every milestone with added delight after enduring such a frightening experience, adding, "Anything is amazing. Spitting up the first solid food is just fantastic!... I think Anna's very excited about them walking and I'm like, 'Just wait - our lives are over once that happens!'"
The twins reached their first birthday last month (Aug13).