A new interfacial instability between two vertical fluid layers of different densities is studied. The two layers are flowing between two parallel vertical plates vertically upward or downward, forming counter- or concurrent flows. In order to extend the study to highly-nonlinear regime in future studies, a nonlinear interface evolution equation is derived, and the stability analysis is performed based on the evolution equation. Among the parameters studies are the ratios of the fluid densities and layer thicknesses and the net flow rate.