We compost many things at home, but cardboard boxes around food are a minefield. Most look like cardboard, but after you compost them you'll be picking out the plastic sheet that was bonded into them. One that particularly annoys me are cat food boxes. The cat food is separately wrapped (in unrecyclable foil-bonded-plastic, of course), and then the cardboard box containing those packets has a hidden plastic layer - for what possible reason!?!

I've been packaging cat food when I was in high school and they do that because, when a single of those cat food packets rips open for whatever reason, the smell is pervasive and intensive. It spreads through the whole warehouse, from a single open bag, getting ever worse as it spoils. The plastic lining in the displays is to protect the shipment - think of an the oilsump the cellar which contains a houses oil tank is lined with. It's a way to contain the spread of a hazardous substance in case the probably containment unit fails.

We shred all cardboard that's not shiny. Generally you can feel if there's a coating. I will also be picking out plastic from our soil for years, but you use the resources you have. It's a worthwhile tradeoff IMHO.