We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending on the electrical properties of the fluids. We also observe that increasing the electric permittivity ratio and decreasing the electrical conductivity ratio, while keeping the rest of the parameters constant, enhances the growth rate of the disturbances. The “Reynolds stress” of the Newtonian layer and the work done by the velocity and stress disturbances tangential to the interface are found to be the mechanism of the instability observed due to the applied electric field. A parametric study is also conducted by varying the thickness of the bottom layer, Bingham number and flow index of the Herschel–Bulkley fluid. Increasing Bingham number is found to be stabilising or destabilising depending on the thickness of the non-Newtonian layer and the maximum disturbance growth occurs at an optimum value of non-Newtonian layer thicknesses. Increasing the shear-thinning and shear-thickening nature is shown to destabilise the flow. Our study is relevant in many microfluidic and electronic cooling applications. © 2020 Elsevier B.V.