The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial eigenvalue is found in closed form by considering the two‐fluid problem as a perturbation of the one‐fluid problem. The importance of the role played by the viscosity difference, when one of the fluids is in a thin layer, is illustrated.