The couple, who celebrated their second wedding anniversary on Oct. 26, are taping a new season of their MTV reality series and will star in their second ABC variety show in December.

Yes, Simpson tells People magazine, they get into arguments.

"What married couple doesn't?" the 24-year-old singer says. "You don't want to marry somebody who's just like you. So there are always going to be conflicts. That's what compromise is all about. It means that we're communicating."

And Lachey, 30, says he isn't jealous of his wife's popularity.

"There's no bigger supporter in Jessica's life than me," he tells the magazine. "Her success is my success. Marriage is a team effort. Both of us share that philosophy."

As to reports that their marriage is on the rocks, Simpson says: "Our relationship is better than it's ever been. We are absolutely not breaking up."

"This is a great time in our lives and careers," Lachey, who grew up in Cincinnati, says.

Meanwhile, Simpson, who will play Daisy Duke in the upcoming The Dukes of Hazzard movie, has come to the defense of her 20-year-old sister, Ashlee, who was recently busted for a Saturday Night Live lip-synch gone awry.

"Ashlee is an amazingly talented person," she told the Access Hollywood syndicated entertainment TV show. "She's already sold 3 million records, which is more than I sold in two years. She's proven herself."