Increasing the spontaneous curvature of an amphiphile can lead to a first-order morphology transition from threadlike micelles to a branched network. The two morphologies were linked to entropy-driven topological defects; networks are dominated by Y-junctions, while linear threadlike structures are dominated by spherical end-caps. In this paper we investigate the effect of mixing on the morphological transitions in nonionic amphiphilic systems. We find that mixed equilibrium structures are obtained within seconds; these mixed cylindrical structures display comparable numbers of end-caps and branch points, resulting in a novel 'short armed' branched (SAB) morphology. Quite surprisingly, the probability of either defect (end-caps or branch points) is independent of composition, so that neither a first-order nor a second-order morphological transition is observed. A possible explanation may be local demixing of the two amphiphilic components, which adds a degree of freedom and thus enables the formation of a unique morphology that cannot be obtained in single-component systems. We further find that within a relatively large composition range phase equilibrium exists between vesicles, SAB micelles, and spherical micelles.