When a dry mass of certain amphiphiles encounters water, a spectacular interfacial instability ensues: It gives rise to the formation of ensembles of fingerlike tubular protrusions called myelin figurestens of micrometers wide and tens to hundreds of micrometers longrepresenting a novel class of nonequilibrium higher-order self-organization. Here, we report that when phase-separating mixtures of unsaturated lipid, cholesterol, and sphingomyelin are hydrated, the resulting myelins break symmetry and couple their compositional degrees of freedom with the extended myelinic morphology: They produce complementary, interlamellar radial gradients of concentrations of cholesterol (and sphingomyelin) and unsaturated lipid, which stands in stark contrast to interlamellar, lateral phase separation in equilibrated morphologies. Furthermore, the corresponding gradients of molecule-specific chemistries (i.e., cholesterol extraction by methyl-β-cyclodextrin and GM1 binding by cholera toxin) produce unusual morphologies comprising compositionally graded vesicles and buckled tubes. We propose that kinetic differences in the information processing of hydration characteristics of individual molecules while expending energy dictate this novel behavior of lipid mixtures undergoing hydration.