An image source method is presented for coherently evaluating the sound field from a point source in flat waveguides with two infinite and parallel locally reacting boundaries, where one is sound absorbing and the other is reflective. The method starts from formulating sound reflections into integrals by plane wave expansion, and the inherent intractability in solving these integrals in such spaces is avoided by introducing a physically plausible assumption that wave fronts remain the same before and after the reflection on a near-rigid boundary. By comparisons to the classical wave theory and the existing coherent ray-based methods, it is shown that the proposed method is considerably accurate to predict the sound propagation in flat waveguides with a sound absorbing ceiling and a reflective floor over a broad frequency range and for various source/receiver geometries, even if at large distances from the source compared to the waveguide height while the existing methods are shown to be erroneous.