As macromolecular surfactants, diblock copolymers order into a variety of morphologies in the presence of a parent homopolymer. Here, we probe the effects of chemical incompatibility and interfacial rigidity on the morphology of copolymer/homopolymer blends at constant blend composition. Five copolymers, each possessing a random-sequence midblock that is varied from 0 to 40 wt% of the copolymer molecular weight, have been synthesized for this purpose. While copolymer micelles are representative of dilute (homopolymer-rich) blends, complex bilayered morphologies, including vesicles and the anomalous isotropic "sponge" phase, are produced upon increasing the midblock fraction. Small-angle neutron scattering provides a quantitative assessment of characteristic microstructural dimensions, while transmission electron microtomography yields the first three-dimensional images of the randomly connected, bilayered membrane comprising the sponge phase.