The phase behavior of poly(ethylene oxide)-poly(butadiene) (PEO-PB) diblock copolymers mixed with water was studied using small-angle X-ray scattering (SAXS), cryogenic scanning electron microscopy (cryo-SEM), cryogenic transmission electron microscopy (cryo-TEM), and dynamic mechanical spectroscopy. Two sets of diblocks were synthesized by adding different lengths of PEO to hydroxy terminated PB with degrees of polymerization NPB = 46 and 170. Two-component mixtures were investigated as a function of block composition and copolymer molecular weight, between 1 and 100 wt % polymer content. Melt phase behavior is consistent with established theory and known experimental behavior for diblock copolymers. Various lyotropic liquid crystalline structures, notably lamellae (L), hexagonally packed cylinders (H), and spheres (S) arranged on cubic (body-centered cubic, face-centered cubic) lattices, were documented as a function of water content. At the higher molecular weights (NPB = 170), a random network phase (N) was identified over a sizable portion of the phase portrait, located between hexagonally ordered cylinders and ordered lamellae. This new structure, along with branching of cylindrical micelles in the dilute limit, bear a striking similarity to experimentally observed and theoretically predicted phase behavior in certain ternary water/oil/surfactant systems. These findings demonstrate that block copolymer surfactants are characterized by at least four structural building blocks-spheres, cylinders, bilayers, and branched cylinders - above a threshold molecular weight.