The Uniform Asymptotic Physical Optics approach is here applied to study the plane wave diffraction by the discontinuity between two co-planar resistive half-sheets. These last possess different surface resistivity, thus causing discontinuities of reflected and transmitted fields. The related coefficients for parallel and perpendicular polarizations are determined by means of the resistive boundary conditions in correspondence of the screens and then applied to the approach. The resulting diffracted field can be used under the rules of the Uniform Geometrical Theory of Diffraction by taking properly into account that the Physical Optics approximation is implemented for the equivalent sources