The swelling and dissolution dynamics of a soluble (small miscibility gap) and an insoluble (large miscibility gap) lamellar phase (L-alpha) of nonionic surfactant in water have been qualitatively and quantitatively investigated. In the case of an insoluble L-alpha, we observe classical myelinic instabilities at the interface. (These are absent in the soluble case.) By doping the excess water phase with colloidal tracer particles, we show that water enters at the roots, rather than through the walls, of the myelins. We estimate the mean water flux and find it to be consistent with this picture. We also study the interface between a lamellar phase and: pure surfactant liquid (L-2), At this interface we observe a new dynamic instability in which "onion jets" appear to be ejected from L-alpha into L-2, where they disappear. Closer investigation shows these onions to be focal conic II defects residing near the surface of a wedge of homeotropic L-alpha, which is in contact with the wall of the sample holder. The defects move much faster than the wedge. We offer some theoretical discussion of how these observations shed light on the mechanism of interfacial instabilities, particularly myelin formation, in surfactant dissolution.