Depth maps produced by consumer-grade sensors suffer from inaccurate measurements and missing data from either system or scene-specific sources. Data-driven denoising algorithms can mitigate such problems. However, they require vast amounts of ground truth depth data. Recent research has tackled this limitation using self-supervised learning techniques, but it requires multiple RGB-D sensors. Moreover, most existing approaches focus on denoising single isolated depth maps or specific subjects of interest, highlighting a need for methods to effectively denoise depth maps in real-time dynamic environments. This paper extends state-of-the-art approaches for depth-denoising commodity depth devices, proposing SelfReDepth, a self-supervised deep learning technique for depth restoration, via denoising and hole-filling by inpainting full-depth maps captured with RGB-D sensors. The algorithm targets depth data in video streams, utilizing multiple sequential depth frames coupled with color data to achieve high-quality depth videos with temporal coherence. Finally, SelfReDepth is designed to be compatible with various RGB-D sensors and usable in real-time scenarios as a pre-processing step before applying other depth-dependent algorithms. Our results demonstrate our approach's real-time performance on real-world datasets. They show that it outperforms state-of-the-art denoising and restoration performance at over 30fps on Commercial Depth Cameras, with potential benefits for augmented and mixed-reality applications.