Ethan Klein's Wife Hila Claims He's Been Having an Affair for 6 Months

"H3 Podcast" host Ethan Klein has been cheating on his wife, Hila Klein, for six months ... at least according to her ... they've separated, and now their show is on indefinite hiatus.

Hila made the bombshell claim on her Instagram, writing ... "I am living a nightmare I can't wake up from. My husband has been having an affair. I have been fed lie after lie after lie for months."

She claims she's had suspicions for a while ... but when she first sensed something was off, Ethan allegedly dismissed her concerns.

Hila says ... "Eventually, he was caught in a lie, and I knew I was done. But the lies continued. 'It was just a kiss' became 'it was emotional cheating.' After I dragged these lies from him, he finally admitted he'd been in an affair for over 6 months, the extent of which I'm sure I still don't know."

Calling the alleged betrayal "immeasurable" ... Hila says she's "in survival mode, trying to navigate separation, co-parenting, and unthinkable heartbreak."

Since Hila made her claims ... the "H3 Podcast" crew announced they would no longer work with Ethan in the wake of the cheating allegations.

They wrote ... "We are all shocked, angry, and heartbroken to learn about Ethan's ongoing affair. As soon as we found out, we all agreed: we would not continue working with Ethan involved or profiting in any way."

They ended their note by writing that they "stand with Hila" and added ... "We're disgusted by Ethan's actions and the hurt he has caused. We all deserved better: Hila, us, and you."

Just last year ... Ethan got Hila's face tattooed on his arm with the message ... "The greatest thing a man can do for his children is to love their mother."

We've reached out to Ethan for comment ... so far, no word back.