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Nick and Jessica: 'We're Not Breaking Up'

11/02/2004 at 06:00 PM EST

Despite rumors that they're on the rocks following a wild bachelor party attended by Nick Lachey on Oct. 12, Newlyweds stars Lachey and Jessica Simpson say that all is fine at home. "Our relationship is better than it's ever been," says Simpson, 24. "We are absolutely not breaking up," adds Lachey.

As for whether Lachey, who turns 31 on Nov. 9, is jealous of his wife's popularity: "There's no bigger supporter in Jessica's life than me," he says. "Her success is my success."

Sure they fight, she says. "You don't want to marry somebody who's just like you," says Simpson. "So there are always going to be conflicts. An argument now and then is good. It means that we're communicating."

The couple, who celebrated their two-year wedding anniversary on Oct. 26, will star in their second ABC variety show on Dec. 10 and are taping the final season of their hit MTV reality series. "This is a great time in our lives and careers," says Lachey.

For more of PEOPLE's exclusive interview, pick up the latest issue on newsstands this Friday.