Hybrid lipid-polymer vesicles can integrate benefits of liposomes and polymersomes. In this work, the phase behavior of hybrid membranes containing lipids and diblock copolymers is explored by dissipative particle dynamics simulations. The influences of lipid unsaturation and thickness mismatch between lipids and polymers are considered. The transition from the mixing state (homogeneous distribution) to the demixing state (formation of bilayered lipid-rich domains) is always observed as the lipid concentration (φ_{l}) exceeds a critical value, which increases with the degree of unsaturation. It is found that phase separation is driven by weak energy incompatibility between the hydrophobic segments of lipids and polymers. When the effect of thickness mismatch becomes significant, the occurrence of the demixing state is retarded, and monolayer lipid rafts emerge before phase separation. Lipid fluidity associated with the physical state of a hybrid membrane can be characterized by lateral lipid diffusivity (D_{l}). In the polymer-rich membrane, D_{l} is higher in the mixing state, but decreases generally with φ_{l} due to lipid-lipid interactions and interdigitation.