I don't think zip codes in practice can be both convex & mutually exclusive.
Imagine a river that divides two zip codes, with river-front property on both sides. If that river has a bend in it (-∿-) that's greater than the width of the river+property, the polygon bounding one zip code would cut through the other, or the polygon is non-convex where it bends along the river.
The Pentagon has six zipcodes and they're divided up by floor.
(My standard example used to be the World Trade Center, which had two - not one for each tower, but one for the state government offices and one for everything else.)