The problem of plane wave diffraction from a plane discontinuity formed by impedance and resistive (or dielectric) half-planes is considered. As is known, diffraction by a two-part surface is an important topic in diffraction theory and is relevant for many applications. This two-part mixed boundary value problem is formulated by Fourier transform technique, and leads to a vector Wiener-Hopf equation which is reduced to scalar form and solved by standard techniques. Then asymptotic expressions for the diffraction coefficients are obtained by evaluating the field integrals asymptotically. These expressions reduce to the known results related to an impedance half-plane when the resistivity (ζ → ∞, which corresponds to the situation where no resistive half-plane exists.