Automated computer vision-based inspections of railway infrastructures, such as component type, damaged status, and location, have been investigated actively by resorting to task-specific deep learning models. However, task-specific models that fulfill these separate inspection tasks encountered bottlenecks in improving inference accuracy, and bring huge computational costs. Multi-task deep learning, which can fulfill these inspection tasks concurrently, has yet to be fully investigated in the context of structural inspection. In this study, a multi-scale task interaction deep learning strategy is presented towards component recognition, damage segmentation, and depth estimation for a comprehensive post-earthquake inspection of high-speed railway viaducts. Three modules for multi-scale task interaction were proposed to modify the multi-task deep neural network, taking full advantage of task commonalities at multiple scales. The proposed method was validated with a large-scale image dataset of high-speed railway viaducts. Component recognition and depth estimation were incorporated to implement multi-task learning since they have higher pattern affinities at multiple scales. Results reported that mean Intersection over Unions of testing samples of component and damage tasks were 91.2% and 72.1%, RMSE of depth estimation was 1.54 m. Compared with single-task cases, training time, inference duration, and FLOPs of the multi-task model were reduced by 23%, 30%, 27% respectively. Results showed improvement in both inference accuracy and training efficiency, substantiating the superiority of the proposed strategy.