The topography and surface composition of thin films (ca. 100 nm) of a polystyrene-b-poly-(ethylene oxide) (PS-PEO) block copolymer are investigated using a suite of complementary techniques, namely tapping mode atomic force microscopy (AFM), optical microscopy, X-ray photoelectron spectroscopy (XPS), neutron reflectometry, and wettability measurements. The copolymer films separate into lamellar structures oriented parallel to the silicon substrate, and bicontinuous and island/hole morphologies characteristic of this arrangement appear. Even though the crystalline topography of the film's surface and its wettability properties suggest the presence of PEO on the top surface, XPS and neutron reflectometry data point undoubtedly to the presence of a top layer of PS at the air/film interface. Tapping mode AFM images unequivocally demonstrate that in air only one block is present at the air/film interface. Neutron reflectometry data identify the nature of each phase-separated layer within the film. This finding differs from a model of domain arrangement proposed in a classic and much-cited paper on these systems (Macromolecules 1979, 12, 323). After exposure to water, PEO blocks rearrange and access the top surface of the film. After many hours of thermal annealing, both PS and PEO blocks can be made to appear at the film/air interface, within isolated droplets formed upon film dewetting.