Amy Robach and T.J. Holmes aren't calling quits on their coupling ... walking arm in arm in NYC -- despite very public tension in their relationship, which we all heard first-hand.

The fired 'GMA3' cohosts took to Instagram Tuesday afternoon to calm fans' minds after they dove headfirst into their behind-the-scenes drama during Monday's episode of their "Amy & T.J." podcast ... where we saw them bickering and arguing on their mics.

Through big grins, and even bigger sunglasses, the happy couple started by reassuring their followers they were still going strong -- saying they struggled over whether to release the episode but ultimately decided to drop it because they wanted to give a comprehensive view of their relationship ... the good, the bad and the awkward.

Amy took it a step further in the caption as well ... once again telling fans she they weren't broken up while plugging the pod -- no such thing as bad publicity we suppose!

ICYMI ... Robach and Holmes laid all their cards on the table ... diving into how they felt in their personal lives with Holmes noting they hadn't slept in the same bed for several days. The convo spiraled into AR mentioning the pressure of her career, and TH outright questioning his better half's communication skills -- not exactly easy listening for fans.

The couple certainly looked happy in the vid they posted ... but they kinda have to put on brave faces, right? Their relationship created both controversy AND this new opportunity for them -- so you figure trouble in paradise could, perhaps, hurt their bottom line.

Anyway, we suppose we'll take their word for it that they're all good now. Based on this, it looks like T.J. & Amy aren't headed to Splitsville ... at least not at the moment.