Water vapor-permeable membranes are finding application in clothing. In this paper membranes prepared from block copolymers of polybutylene terephthalate (PET) and polyethylene oxide (PEOX) are introduced from a structural perspective. The block copolymers are processed into dense membranes by melt-extrusion. In the solid state the PET and PEOX blocks are segregated into a two-phase domain structure in which both phases are continuous. The polymer shows a spherulitic-like morphology caused by the crystalline PET submatrix, which provides strength, stability and processibility. The flexible and polar PEOX submatrix provides for a high permeability of water and an elastomeric character. The polymer composition (block ratio and block length) strongly affects the final membrane properties and can be used for optimizing conflicting properties like permeability and mechanical stability.