The conformation of the lung surfactant lipid bilayer (termed tubular myelin) is shown to fit an infinite periodic surface, which is free from self-intersections and with zero or close to zero average curvature. A single lipid bilayer is curved in space, forming a tetragonal structure (CLP) with tubular units, the walls of which are close to planar and parallel to two orthogonal directions. A cryo transmission electron microscopy (cryo-TEM) study of the alveolar surface layer from rabbit was performed. Direct deposition of the surface layer on the microscopy grid indicates that the surface zone consists of a homogeneous phase. The cryo-TEM texture of the bilayer is consistent with earlier reported electron microscopy observations of dispersed aggregates in lung washings. It is shown how the interface towards air can be formed by opening up the phase along lipid methyl end groups. The model is fundamentally different from earlier proposals, involving a “free” lipid-protein monolayer at the air/water interface. Functional aspects and medical implications of a coherent surface phase structure are discussed.