Mariah Carey and Nick Cannon ... We Still Break Bread as a Family

Mariah Carey and Nick Cannon have quietly figured out how to remain a family for the sake of their kids ... and they successfully spent the first big holiday together since they separated.

Mariah made it SEEM like Thanksgiving was Cannon free ... posting a pic of her in the foyer of a home.

But we know not only was Nick there ... it was HIS L.A. home.

Our Carey/Cannon sources say their relationship was extremely toxic when they were together, but they actually get along as friends now and both are committed to the welfare of their 3-year-old twins.

We're told Thanksgiving was calm and happy, although Mariah and the kids bolted for a hotel after the meal.

As for how the kids are doing ... we're told they're not really conscious or affected by the separation, because they're used to being cared for by one parent or the other ... interaction with both Mariah and Nick was infrequent over the last 3 years.