We experimentally study the cavities forming in the wake of rigid spheres when submerging into a stratified, two-layer system of immiscible, quiescent liquids comprising a thin layer of oil above a deep pool of water. The results obtained for our two-layer system are compared with data from the literature for the corresponding type of cavities formed when spheres enter a homogeneous liquid that is not covered by an oil layer. The discussion and the data analysis reveal that the oil coating acquired by the spheres while propagating through the thin oil layer, before entering the pool of water underneath, substantially affects qualitative and quantitative aspects of the dynamics associated with the cavity formation. In particular, we observe the formation of a ripple-like pattern on the cavity walls which is not known to exist when spheres enter a homogeneous liquid. The data analysis suggests that the ripple patterns form as a consequence of a two-dimensional instability arising due to the shear between the oil layer coating the spheres and the ambient water.