Lamellar to nonlamellar membrane shape transitions play essential roles in key cellular processes, such as membrane fusion and fission, and occur in response to external stimuli, including drug treatment and heat. A subset of these transitions can be modeled by means of thermally inducible amphiphile assemblies. We previously reported on mixtures of hydrogenated, fluorinated, and hybrid Janus dendrimers (JDs) that self-assemble into complex dendrimersomes (DMSs), including dumbbells, and serve as promising models for understanding the complexity of biological membranes. Here we show, by means of a variety of complementary techniques, that DMSs formed by single JDs or by mixtures of JDs undergo a thermally induced lamellar-to-sponge transition. Consistent with the formation of a three-dimensional bilayer network, we show that DMSs become more permeable to water-soluble fluorophores after transitioning to the sponge phase. These DMSs may be useful not only in modeling isotropic membrane rearrangements of biological systems but also in drug delivery since nonlamellar delivery vehicles can promote endosomal disruption and cargo release.