Liposomes grafted with polymer have long been used in drug delivery applications, and block copolymersomes have emerged as attractive and more robust alternatives for both drug delivery and artificial organelle applications. Hybrid membranes that could combine the respective advantages of fluid lipid and robust polymer bilayers are an attractive and enticing alternative. The properties of membranes in amphiphile vesicles are challenging to study and many applications benefit from surface-based access to the membrane. We therefore explore the self-assembly and mechanical properties of supported hybrid bilayers (SHBs) composed of polybutadiene-block-poly(ethylene oxide) block copolymers and zwitterionic phosphatidylcholine lipids on SiO2 supports. Quartz crystal microbalance with dissipation monitoring (QCM-D) measurements show that formation of SHB on SiO2 by vesicle fusion depends on the mass fractions of lipids and block copolymers. Atomic force microscopy was used to study the microscopic mixing of lipids in the SHB to reveal that lipid-phase separation is not observed in SHBs. Force spectroscopy was performed to extract information about thickness and mechanical properties of the hybrid membranes. SHBs are shown to combine the properties of lipid membranes and polymer brushes, and the tip force required to rupture the membrane decreases and the bilayer thickness increases as the block copolymer fraction is increased.