Semantic segmentation methods based on deep neural networks have achieved great success in recent years. However, training such deep neural networks relies heavily on a large number of images with accurate pixel-level labels, which requires a huge amount of human effort, especially for large-scale remote sensing images. In this paper, we propose a point-based weakly supervised learning framework called the deep bilateral filtering network (DBFNet) for the semantic segmentation of remote sensing images. Compared with pixel-level labels, point annotations are usually sparse and cannot reveal the complete structure of the objects; they also lack boundary information, thus resulting in incomplete prediction within the object and the loss of object boundaries. To address these problems, we incorporate the bilateral filtering technique into deeply learned representations in two respects. First, since a target object contains smooth regions that always belong to the same category, we perform deep bilateral filtering (DBF) to filter the deep features by a nonlinear combination of nearby feature values, which encourages the nearby and similar features to become closer, thus achieving a consistent prediction in the smooth region. In addition, the DBF can distinguish the boundary by enlarging the distance between the features on different sides of the edge, thus preserving the boundary information well. Experimental results on two widely used datasets, the ISPRS 2-D semantic labeling Potsdam and Vaihingen datasets, demonstrate that our proposed DBFNet can achieve a highly competitive performance compared with state-of-the-art fully-supervised methods. Code is available at https://github.com/Luffy03/DBFNet.