We introduce the design and study of a hybrid electrospun membrane with a dedicated nanoscale structural hierarchy for controlled functions in the biomedical domain. The hybrid system comprises submicrometer-sized internally self-assembled lipid nanoparticles (ISAsomes or mesosomes) embedded into the electrospun membrane with a nanofibrous polymer network. The internal structure of ISAsomes, studied by small-angle X-ray scattering (SAXS) and electron microscopy, demonstrated a spontaneous response to variations in the environmental conditions as they undergo a bicontinuous inverse cubic phase (cubosomes) in solution to a crystalline lamellar phase in the polymer membrane; nevertheless, this phase reorganization is reversible. As revealed by in situ SAXS measurements, if the membrane was put in contact with aqueous media, the cubic phase reappeared and submicrometer-sized cubosomes were released upon dissolution of the nanofibers. Furthermore, the hybrid membranes exhibited a specific anisotropic feature and morphological response under an external strain. While nanofibers were aligned under external strain in the microscale, the semicrystalline domains from the polymer phase were positioned perpendicular to the lamellae of the lipid phase in the nanoscale. The fabricated membranes and their spontaneous responses offer new strategies for the development of structure-controlled functions in electrospun nanofibers for biomedical applications, such as drug delivery or controlled interactions with biointerfaces.