Amphiphilic compounds such as lipids and surfactants are fundamental building blocks of soft matter. We describe experiments with poly(1,2-butadiene-bethylene oxide) (PB-PEO) diblock copolymers, which form Y-junctions and three-dimensional networks in water at weight fractions of PEO intermediate to those associated with vesicle and wormlike micelle morphologies. Fragmentation of the network produces a nonergodic array of complex reticulated particles that have been imaged by cryogenic transmission electron microscopy. Data obtained with two sets of PB-PEO compounds indicate that this type of self-assembly appears above a critical molecular weight. These block copolymers represent versatile amphiphiles, mimicking certain low molecular weight three-component (surfactant/water/oil) microemulsions, without addition of a separate hydrophobe.