"It feels good to have the ring on my finger," the Avett Brothers rocker says of marrying the former Dexter actress
Credit: DRILA/Broadimage

The Avett Brothers titled their latest album True Sadness – but singer-guitarist Seth Avett’s life is quite the opposite these days.

The Americana rocker, 35, married Limitless actress Jennifer Carpenter, 36, in an an intimate North Carolina ceremony over Memorial Day weekend – a step in their relationship that felt natural for the pair.

“It feels like there’s a weight lifted off my shoulders ’cause we’ve thought about it for so long, and it’s nice to make it official,” Seth tells PEOPLE.

The rocker and Carpenter said their “I Do’s” about a year after welcoming their first child together, son Isaac, last year.

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“It feels very right, and it feels good to have the ring on my finger,” adds Seth, who went public with his relationship with Carpenter in 2013. “We’re just under a month now. I don’t know that it’s changed me, but there’s a settling logistically and a settling in my mind that’s getting beyond the wedding.”

As for their North Carolina nuptials, the musician says he had some pre-wedding jitters going into the big day – but only from a planning standpoint because “there’s a certain level of anxiety that comes with it.”

“I was probably more specific about how I wanted it to go than Jennifer was. She’s much more laid back with all of that,” Seth adds with a laugh. “I don’t know if I turned into a groomzilla, but I was definitely a little more involved in, like, ‘No, not those candles – these candles!'”

As Seth settles into married life as a father, he has some pals he can identify with – because his band with brother Scott is now on the road touring in support of True Sadness.

While the North Carolina-bred collective has been been together for 16 years, Seth says his new family “has just been one more element that united us in a way,” as Scott has three kids and bassist Bob Crawford has two.

“Up until a year ago, it was still an abstract concept. I had sympathy and an intellectual understanding of why they were so torn up when we got on the road and why they felt a different kind of pain or longing to be home that I didn’t, but I couldn’t really wrap my head around it,” Seth says.

After welcoming Isaac in February last year, that changed.

“I get it now. It’s a deeper level of feeling to miss your child, who’s at home growing and changing every day, and you’re just getting a picture or video or the occasional FaceTime. It’s not the same as being there to pick them up,” Seth adds. “In terms of our connection as a band, it’s one more thing that we can talk about and learn from each other.”

And while his new wife is a big fan and comes to shows, Seth says he’s not sure about his son – at least yet!

“He definitely loves music – you can snap your fingers, and he’ll start dancing. But I don’t know if Isaac’s a fan of my music, specifically,” says Seth. “But he’s a fan of me as Dada for sure!”

Meanwhile, Scott, 40, says he has some young musicians in his growing brood, too.

“We do encourage show-stardom in our household,” he says with a laugh, referencing daughter Eleanor, 7, and sons Max, 5, and 1-year-old Luke. “We encourage the kids to get on the coffee table and put on a show anytime they want and encourage them in the arts in all ways.”

So does the rocker think his kids will follow in his footsteps?

“Who knows? When you grow up in a place like we did that was blue-collar, the reality of what could be your future was other things – great things that I admire quite a bit,” Scott says.

“I could not be prouder if my son was a carpenter or if my daughter was a teacher or if my son was a nurse – what could be better? We were told by our dad when we were kids: ‘No matter what you do, you’re gonna be the best at it, and I’m gonna be proud of you.'”