We show the existence under shear flow of steady states in a two-phase regi
on of a brine-surfactant system in which lyotropic dilute lamellar (non-New
tonian) and sponge (Newtonian) phases are coexisting. At high shear rates a
nd low sponge phase-volume fractions, we report on the existence of a dynam
ic transition corresponding to the formation of a colloidal crystal of mult
ilamellar vesicles (or "onions") immersed in the sponge matrix. As the spon
ge phase-volume fraction increases, this transition exhibits a hysteresis l
oop leading to a structural bistability of the two-phase flow. Contrary to
single phase lamellar systems where it is always 100%, the onion volume fra
ction can be monitored continuously from 0 to 100 %.