The couple welcomed its first child, son Hayes Andrew, in late March, and the "Girl" hitmaker subsequently revealed she had to undergo an emergency C-section to safely deliver the tot after spending 30 hours in labour.
Morris and Hurd have been focused on bonding with their little one at their new Nashville, Tennessee home during the coronavirus pandemic, having already planned to take time off after the baby's arrival.
"Life isn't that different from the way that we planned it, to be honest. We were going to be off the road right now," Hurd tells People.com.
"It's a little harder because we can't really have anybody over to see our baby, but I feel like we're very blessed in that we have avoided a lot of hardships that other artists have had to face, because we haven't had to really cancel many shows."
"We're really lucky to just be here learning how to be a family of three and it's been really an amazing time in our lives."
Gushing about fatherhood, Hurd adds, "You imagine what it's going to be like, and then it ends up happening - and it feels like you couldn't imagine ever going back to just being the two of you. So we're really lucky to have him here and have both of them healthy."
And the first-time dad is keeping busy making sure Morris doesn't over-extend herself post-surgery: "(Maren is) recovering still, so we try to make sure she's off her feet as much as I can. She's not very patient...!"
"The whole first month has sort of been making sure that her relationship with this kid is rock solid and making sure that he's supported," Hurd continues. "I change a lot of diapers, and I keep my hands constantly busy cleaning or making bottles and stuff like that."
"It's mostly just made me hyper-aware of my responsibility to the two of them...," he shares of how becoming parents has strengthened their marriage. "There's just another part of the equation now."
Hurd and Morris wed in 2018 after five years together.