The aerial energy transmission system is currently advancing towards autonomy and intelligence, with a focus on the key technology of visually perceiving the hose and drogue components integral to the system. In addressing this challenge, we proposed a three-dimensional reconstruction method based on a hybrid binocular vision model and data driven approach in this paper. Specifically, a novel multi-task deep convolutional neural network was designed for target detection and disparity estimation, to achieve accurate detection and three-dimensional reconstruction of the transmission hose and drogue device. Additionally, a blender-based approach was introduced for generating images in the context of aerial energy transmission scenarios, enabling automated generation and annotation of stereo image samples to construct a comprehensive dataset. Finally, extensive training and testing were conducted on the established aerial energy transmission scene dataset, demonstrating good performance of the proposed method.