Dense depth information can be reconstructed from stereo images using conventional hand-crafted as well as deep learning-based approaches. While deep-learning methods often show superior results compared to hand-crafted ones, they commonly learn geometric principles underlying the matching task from scratch and neglect that these principles have already been intensively studied and were considered explicitly in various models with great success in the past. In consequence, a broad range of principles and associated features need to be learned, limiting the possibility to focus on important details to also succeed in challenging image regions, such as close to depth discontinuities, thin objects and in weakly textured areas. To overcome this limitation, in this work, a hybrid technique, i.e., a combination of conventional hand-crafted and deep learning-based methods, is presented, addressing the task of dense stereo matching. More precisely, the input RGB stereo images are supplemented by a fourth image channel containing feature information obtained with a method based on expert knowledge. In addition, the assumption that edges in an image and discontinuities in the corresponding depth map coincide is modeled explicitly, allowing to predict the probability of being located next to a depth discontinuity per pixel. This information is used to guide the matching process and helps to sharpen correct depth discontinuities and to avoid the false prediction of such discontinuities, especially in weakly textured areas. The performance of the proposed method is investigated on three different data sets, including studies on the influence of the two methodological components as well as on the generalization capability. The results demonstrate that the presented hybrid approach can help to mitigate common limitations of deep learning-based methods and improves the quality of the estimated depth maps.