Coated Cardboard - compost material, fuel source, or recycling?

I was wondering about all of the coated cardboard that is ending up in our recycling bin - while I strive to purchase only glass when I can, the others living with me are not as eco-minded and even for myself, it's hard to avoid plastic and coated cardboard entirely.

Are there any uses for coated cardboard that is better than sending it through the recycling process? I have tried looking it up and there seems to be disagreement on what exactly the cardboard is coated with (plastic, clay, wax, etc) so I thought I would ask here and see if anyone has any suggestions.

Composting would be my preferred method if it's safe for me and the environment (and it actually breaks down), but otherwise I am open to other options!

I'm not inclined to put unknowns in my compost or garden. So for me, anything coloured or coated goes to recycling.

"Coated cardboard" is such a wide range of stuff. Did you have a particular one in mind?

Some examples...
Aseptic cartons: Milk, juice may be plastic coated? the TetraPak versions (like chicken broth boxes) may also have an aluminum foil component? Some municipal recycling accepts them, others not. These could take a turn as seedling pots before the trash...
Fruit/vegetable crates/cold cups: Waxed. Probably great for burning, composts in industrial hot-composting, not sure if that's a good thing, other than being easy to manage grocery waste, since it is usually NOT mixed with Kraft cardboard or other papers due to the wax.
Take-out stuff: boxes, hot cups, microwaveable trays... probably all plastic coated? Usually paper in direct contact with food, not recyclable.
Chipboard cereal boxes, cracker boxes, etc...: Clay coated.

Lots of recycling rules are also geared towards compliance, versus recyclability. This is mostly to avoid food contamination. A pizza box is perfectly recyclable, but too many boxes also contain the oily disc/paper liner, a "pizza table", and some uneaten parts of the pizza, so it can be called out as "not accepted" since it spoils the rest of the stuff.

It is a very wide range, but my hope is to have an understanding of "what to do with cardboard that is coated with x", as well as a way to determine the coating type if possible.

Some examples of boxes in question:
Cereal boxes, milk cartons, "freezer" boxes (like frozen pizza), cracker boxes, medicine boxes, soda can boxes, and boxes from electronics.