"Like most people, I have male and female friends and I'm not going to end my friendships just because I'm on TV," he says in a statement. "However, being out with them late at night showed poor judgment on my part. What makes me sick is that my careless behavior has put my family in this uncomfortable position. My family is the most important thing in my life and it kills me that these allegations have hurt them."
The Gosselins, who are raising 8-year-old twins and 4-year-old sextuplets, have dealt with similar allegations in the past. In February, Jon was spotted hanging out with a couple of female college students from Juniata College, located near his hometown in Pennsylvania.
But a couple of girls who met Jon that night said he didn't flirt with anyone. "He was very well-behaved, a gentleman," Alex-Rae Campbell, a college student who attended the party, told PEOPLE. "He talked more about his wife than his kids. He was very friendly, very approachable."
Shortly after, the couple told PEOPLE that raising their children in public has been stressful for their marriage. "Kate's career is taking off and I'm a bit lost," Jon admited. "This struggle has definitely put some tension in our marriage."
With reporting by KATHY EHRICH DOWD