Jon & Kate

The pair both share a love ... for gray jackets.

A local radio DJ said he spotted Kate and Steve holding hands last week -- but Steve was ninth in line to get that kinda treatment while the whole family -- minus Jon -- was at a park in Penn. yesterday.

Jon Gosselin and the rest of the clan spend some quality time together -- presumably while Mom gives another interview about her hair.

According to Detroit radio personality Mojo from Mojo in the Morning, "Jon & Kate Plus 8's" Kate Gosselin is getting hands on with her bodyguard -- and he saw it with his own eyes!

Mojo says he saw Kate and her busted weave last night at the Marriott with her hired protector, Steve Neild ... and they were holding hands!

Kate (and her hair) was left to defend her hubby's actions all by her lonesome -- which she only kinda sorta did. Kate also told Meredith Viera that she and Jon -- who both star on a reality show which documents every minute detail of their lives -- will deal with this situation in private.

One of them had marital problems and divorced her husband.

The reality television father of eight has allegedly been having an affair with a third grade teacher, Us Weekly is reporting. The two reportedly met at a bar back in mid-January.

The alleged other woman's brother tells the mag his sister is not a homewrecker, but adds this TMI detail -- "A lot of the time, it was pretty, um, gross listening to her, you know, um -- how do I say this? The walls are thin. Let's just say that. I mean, no one wants to hear his sister having sex, let alone with a married dude who's, like, almost twice her age and who has eight kids and a maybe-crazy wife. Ick. Nast."

We got Kate Gosselin yesterday in New York -- where she kept quiet about the alleged "nast" hookup.

Though a rep, Jon told us, "These allegations are false and just plain hurtful. As I adjust to the the attention that comes from being in the public eye, I need to be more careful and aware of who I am associating with and where I am spending my time. But the bottom line is, I did not cheat on Kate. I am sorry for putting my family in this awkward position, given some poor decisions and bad judgements I've made recently. I am working through this difficult time with my family. My family is my top priority."

While pics surfaced of Jon leaving a nightclub with a lady friend last week, the not-so-happy couple appeared together at something called the Pennsylvania Women's Show this weekend.

Although Jon claims the woman was just a friend, he did admit his actions "showed poor judgement" ... much like Kate's choice in hairstyles.

When asked about their relationship, Kate Gosselin told our camera "We're good."