We analyze the electrorheological effect in immiscible fluid mixtures with dielectric mismatch. By taking the electric field effect into account, which couples to the dynamics of domain morphology under flow, we propose a set of electrorheological constitutive equations valid under the condition where the relative magnitude of the flow field is stronger than that of the electric field. Through comparison with recent experiments, we point out a unique dynamical stress response inherent in situations where the cross-coupling between different fields is essential.