The propagation of gravitational waves between two semi-infinite superposed electrorheological fluids is investigated, Criteria for stability in the presence of a vertical or a horizontal electric field are examined. A modified Chandrasekhar transcendental dispersion relation is obtained, Stability analysis is discussed throughout the case of a small dimensionless phase velocity. The influence of the nondimensional parameters on the growth rate of the Rayleigh-Taylor instability is discussed. The behavior of the growth rate with respect to the stratified viscosity, as well as the stratified retardation time in the presence or absence of an electric field, is investigated. It is shown that a vertical electric held retards the stabilizing influence of both the retardation time and the viscosity, while the presence of a tangential field suppresses the destabilizing influence of the stratified density. A mechanism that shields against the destabilizing influence of the vertical electric field is observed. This shielding mechanism is due to viscous and elastic effects.