In this paper, we tackle the depth completion problem. Conventional depth sensors usually produce incomplete depth maps due to the property of surface reflection, especially for the window areas, metal surfaces, and object boundaries. However, we observe that the corresponding RGB images are still dense and preserve all of the useful structural information. This brings us to the question of whether we can borrow this structural information from RGB images to inpaint the corresponding incomplete depth maps. In this paper, we answer that question by proposing a Disentangling and Exchanging Network (DEN) for depth completion. The network is designed based on an assumption that after suitable feature disentanglement, RGB images and depth maps share a common domain for representing structural information. So we firstly disentangle both RGB and depth images into domain-invariant content parts, which contain structural information, and domain-specific style parts. Then, by exchanging the complete structural information extracted from RGB image with incomplete information extracted from depth map, we can generate the complete version of depth map. Furthermore, to address the mixed-depth problem, a newly proposed depth representation is applied. By modeling depth estimation as a classification problem coupled with coefficient estimation, blurry edges are enhanced in the depth map. At last, we have implemented ablation experiments to verify the effectiveness of our proposed DEN model. The results also demonstrate the superiority of DEN over some state-of-the-art approaches.