We describe a distinct type of spontaneous hierarchical self-assembly of cytoskeletal filamentous actin (F-actin), a highly charged polyelectrolyte, and cationic lipid membranes. On the mesoscopic length scale, confocal microscopy reveals ribbonlike tubule structures that connect to form a network of tubules on the macroscopic scale (more than 100 micrometers). Within the tubules, on the 0.5- to 50-nanometer length scale, x-ray diffraction reveals an unusual structure consisting of osmotically swollen stacks of composite membranes with no direct analog in simple amphiphilic systems. The composite membrane is composed of three layers, a lipid bilayer sandwiched between two layers of actin, and is reminiscent of multilayered bacterial cell walls that exist far from equilibrium. Electron microscopy reveals that the actin layer consists of laterally locked F-actin filaments forming an anisotropic two-dimensional tethered crystal that appears to be the origin of the tubule formation.