Actually, the current Seattle recycling sheet says that food-soiled coated paper goes in the trash. If your take-out containers aren't waxed, they can go in yard waste. It's complicated -- I keep the flyer up on our fridge for easy reference.

http://www.seattle.gov/util/Services/Recycling/LookupTool/FoodPackaging/BoxesCartonsLiners/Take-OutContainers/index.htm

http://www.seattle.gov/util/stellent/groups/public/@spu/@csb/documents/webcontent/spu02_014944.pdf (5MB pdf)