We investigated the electrorheological (ER) properties of a mixture of two immiscible fluids having the same viscosity, but different permittivity and conductivity. In this mixture droplets were dispersed; when subjected to an electric field they became elongated. We observed an ER effect, i.e., an increase in the apparent viscosity following application of an electric field. It was seen from microscopic observation that the ER effect in the mixture is brought about by a morphological change, with the interfacial tension between the two fluids playing a crucial role.