The vortex structure of immiscible liquid-liquid Taylor-Couette-Poiseuille flow was studied using photographic techniques. Several parameters were considered, including the feed composition and the inner cylinder rotation rate. For certain feed compositions and sufficiently large rotation rates a translating banded structure, which consisted of alternating aqueous and organic-rich vortices, persisted indefinitely. At lower rotation rates, either a spatially homogeneous emulsion evolved or sustained oscillations between the banded and homogeneous structures developed.