Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction.