Matt Lauer and Wife Angrily Deny Breakup Report

Matt Lauer and his wife Annette are blasting a report they have split, and the Today co-host calls the tabloid story alleging he had moved out of his family's apartment "a work of fiction."

"I am living in my apartment with Annette and my children as a family and a couple," Lauer tells PEOPLE exclusively in an interview from France, where he's been co-anchoring the NBC morning show from the Cannes Film Festival. "I have never moved out. I am not moving out. There is no truth to that."

Annette Lauer says in a separate interview with PEOPLE, "Out of self respect, I want to stand up for our family and protect them."

Lauer, who has been dogged by stories of reported infidelity – and whose wife, a former model, briefly filed for divorce in 2006 – acknowledges past difficulties in the 12-year marriage. But he labels as "ridiculous" and "offensive" reports he had ever cheated on her.

Marriage Not Perfect
"Have we had a completely perfect, easy marriage? No. But the stories you've read over the years are not true," Lauer said.

"I don't think we're any different than any married couple that's been together for 12 years," he adds. "The accusations [of infidelity] are ridiculous and I'm not going to [dignify] them with an answer. It's not true."

Annette Lauer also acknowledges past marital difficulties, but says, "We have worked through it."

"All Made Up"
Lauer takes specific issue with numerous points in this week's National Enquirer cover story, which claims he was partying almost nightly in Vancouver during the Winter Olympics, delayed his return to New York to continue his night-crawling, and missed Valentine's Day back home with his wife.

In fact, says Lauer, his wife and three children were with him on Feb. 14 skiing at the Whistler resort near Vancouver. As for the partying, Lauer notes that he was getting up at 1:30 a.m. to make it to Today's Olympic set for broadcasts that began at 4 a.m. local time. As a result, he was in bed most nights by 7:30 p.m.

He also says he returned to New York two days before the rest of the Today staff. "This is all made up," Lauer says. "All they had to do was check."