Lipids and block copolymers can be individually assembled into unsupported, spherical membranes (liposomes or polymersomes), each having their own particular benefits and limitations. Here we demonstrate the preparation of microscale, hybrid "lipopolymersomes" composed of the common lipid POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine) and the commercially available copolymer PBd-b-PEO (polybutadiene-b-poly(ethylene oxide)) with the goal of incorporating the advantageous qualities of the unitary systems into mixed-membrane capsules. We investigate the lipopolymersomes using confocal fluorescence microscopy and demonstrate that these hybrid membranes are well mixed on nanoscopic length scales within the permittable compositional windows for hybrid vesicle formation. We measure the intramembrane dynamics and mechanical properties of these hybrid membranes by fluorescence recovery after photobleaching (FRAP) and micropipet aspiration, respectively. For the first time, we demonstrate the demixing of lipid-rich and polymer-rich membrane domains within the same vesicle membrane. This is achieved by the biotinylation of one of the constituent species and cross linking with the protein NeutrAvidin. The resultant domain patterning is dependent upon which component carries the biotin functionality: cross linking of the copolymer species results in domains that ripen into a single, large, copolymer-rich island, and cross linking of the lipids yields many small, "spot-like", lipid-rich domains within a copolymer-rich matrix. We discuss these morphological differences in terms of the fluidity and mechanical properties of the membrane phases and the possible resultant interdomain interactions within the membrane. These heterogeneous hybrid lipopolymersomes could find applications in fields such as targeted delivery, controlled release, and environmental detection assays where these capsules possess the characteristics of biocompatible lipid membranes combined with enhanced mechanical strength and stability from the copolymer matrix.