Solutions to two coupled half‐plane problems are derived. In the first, an exact solution to the canonical problem of acoustic plane‐wave diffraction from a pressure release (zero impedance) surface coupled to a perfectly rigid (infinite impedance) surface is given using the Wiener–Hopf method. The solution is expressed in terms of an angular spectrum of plane waves. In the second, the rigid surface is replaced by one characterized by a locally reacting finite impedance. Here, an approximate kernel to the Wiener–Hopf functional equation is used which leads to a complete and readily interpretable solution. This solution is expressed in terms of the canonical angular spectrum for the first problem multiplied by a function that depends on material parameters of the locally reacting surface. Polar plots of the far‐field amplitude level for the diffracted field are presented.