Hybrid polymer/lipid large unilamellar vesicles (LUVs) were studied by small angle neutron scattering (SANS), time-resolved Förster resonance energy transfer (TR-FRET), and cryo-transmission electron microscopy (cryo-TEM). For the first time in hybrid vesicles, evidence for phase separation at the nanoscale was obtained, leading to the formation of stable nanodomains enriched either in lipid or polymer. This stability was allowed by using vesicle-forming copolymer with a membrane thickness close to the lipid bilayer thickness, thereby minimizing the hydrophobic mismatch at the domain periphery. Hybrid giant unilamellar vesicles (GUVs) with the same composition have been previously shown to be unstable and susceptible to fission, suggesting a role of curvature in the stabilization of nanodomains in these structures.