That box is coated to make it water-resistant. Technically they can be separated and the paper half recycled, but almost no municipality does it.

I'm talking about the powder detergent. (Liquid detergent inherently wastes resources hauling water around. I already have water.) The inside of the box is just cardboard. The outside is printed with some sort of glossy image, but I don't see how it's qualitatively different than a cereal box...