The co-assembly of lipids and block copolymers is a new strategy to enable materials with nanostructure complexity as well as responsive transport and mechanical behavior. In water, lipids adopt a variety of structures including bicontinuous cubic phases that are highly desirable for numerous biotechnological applications and separation membranes. Block polymers assemble into analogous mesophases but do not always require aqueous media. Using grazing incidence small-angle X-ray scattering (GISAXS) and atomic force microscopy (AFM), we show that monoolein (MO), 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP), and poly(butadiene-b-ethylene oxide) (PBD-b-PEO) self-organize into highly ordered bicontinuous cubic phases without the need of an aqueous environment. Ternary MO/DOTAP/PBD-b-PEO systems exhibit hybrid bilayer networks separating periodic arrays of nonpenetrating channels retaining water from air humidity. We attribute this behavior to positively charged lipids that in cooperation with block copolymers can pin ambient hydration, demonstrated by coarse-grained simulations. Our study broadens the understanding of the structural diversity of lipid−polymer hybrid materials, opening the potential of designing new biocompatible humidity-responsive nanomaterials.