The couple, who have three children, got married in 2012 after six years together.
He told GQ magazine: "We did a lot of reading and talked to a lot of people that had been divorced, a lot of people that had been happily married. We talked to our pastor.
"I had to get to the point where I saw [getting married] as more than just the thing to do," the actor said.
"I wanted to really want to. You know, I didn't want it to be just a destination; the fun is that we're on the adventure together."
"In the end, our understanding was, Let's go make a covenant, with you, me, and God."
The actor thanked God when he won his Best Actor Oscar at the 2013 Academy Awards for his lead role in Dallas Buyers Club.
On receiving the award, he said: "He has graced my life with opportunities that I know are not of my hand or of any other human hand."