Solvent cast diblock and triblock copolymer films of poly(ethylene oxide-b-styrene) (PEO-b-PS) and poly(ethylene oxide-b-methyl meth acrylate-b-styrene) (PEO-b-PMMA-b-PS), with cylindrical microdomains of PEO or PMMA-PEO, have a high degree of lateral ordering after solvent annealing. The relative humidity of the vapor during the solvent annealing has been shown to play an important role in achieving this order. After solvent annealing under high humidity a PEO-b-PMMA-b-PS triblock copolymer having a lamellar morphology in bulk develops a hexagonal array of depressed PEO domains on the film surface while the film surface remains flat under less humid conditions. Cross-sectional TEM and GISAXS show that the film annealed under high humidity conditions exhibits a well-defined hexagonally perforated lamellar (HPL) structure throughout its thickness, whereas a stack of lamellae aligned parallel to the surface is evident for films annealed at lower humidity. These results demonstrate the switchable nanoscopic structure of these films and strongly suggest that water vapor induces the morphological transition from lamellar to HPL by swelling the PEO domains.