Hierarchic self-assembly is the main mechanism used to create diverse structures using soft materials. This is a case for both synthetic materials and biomolecular systems, as exemplified by the non-covalent organization of lipids into membranes. In nature, lipids often assemble into single bilayers, but other nanostructures are encountered, such as bilayer stacks and tubular and vesicular aggregates. Synthetic block copolymers can be engineered to recapitulate many of the structures, forms, and functions of lipid systems. When block copolymers are amphiphilic, they can be inserted or co-assembled into hybrid membranes that exhibit synergistic structural, permeability, and mechanical properties. One example is the emergence of lateral phase separation akin to the raft formation in biomembranes. When higher-order structures, such as hybrid membranes, are formed, this lateral phase separation can be correlated across membranes in the stack. This chapter outlines a set of important methods, such as X-ray Scattering, Atomic Force Microscopy, and Cryo-Electron Microscopy, that are relevant to characterizing and evaluating lateral and correlated phase separation in hybrid membranes at the nano and mesoscales. Understanding the phase behavior of polymer-lipid hybrid materials could lead to innovative advancements in biomimetic membrane separation systems.