The present study concerns the formation and structure of aqueous dispersions of lipid-based lyotropic Liquid crystalline phases, namely reversed types of hexagonal and bicontinious cubic phases. As stabilizer a nonionic triblock polymer proves to be efficient for dispersions of both phases. We demonstrate that these dispersions contain submicron particles with a preserved inner periodicity. The morphology and inner structure of the dispersed particles are characterized by means of SAXS (small-angle X-ray scattering) and cryo-TEM (cryo-transmission electron microscopy). The particle shape is shown to reflect the crystallinity of the lipid structure. Thus the morphology of particles from cubic phases differs from that of the ones obtained from the hexagonal phase. Furthermore, an interesting difference is found in the partitioning of the polymer in the two types of dispersions. The polymer is localized within the core as well as at the surface of the dispersed particles of the cubic phase, whereas the core of the particles from the hexagonal phase seems depleted of polymer at the same polymer concentration.