Jessica Simpson's parents to divorce

Jessica Simpson's parents, Tina and Joe Simpson, are headed for a divorce after 34 years of marriage.

The family's rep told People: "It is an amicable split and there is no third party involved. Any other related allegations are completely false. The family appreciates your respect for their privacy at this time."

It's unclear which allegations the rep was referring to, but the divorce news comes as the National Enquirer reports that Joe has "confessed" that he's gay, a story that appears to be just a tabloid rumor.

According to TMZ, Tina, 52, filed for divorce on Sept. 24, in McLennan County, Texas, noting, "The marriage has become insupportable because of discord or conflict of personalities."

The 54-year-old Joe, or "Papa Joe" as he's been called, was arrested on suspicion of DUI this summer in Sherman Oaks, Calif. He pleaded not guilty.

Joe has been heavily involved in the lives and careers of his daughters, Jessica and Ashlee Simpson.

Earlier this week, he tweeted about Ashlee's son: "Spent the day with Bronx. Just reminded what a blessing it is to be a papa!!"