Power lines are dangerous for low-flying aircraft, especially in low-visibility conditions. Thus, a vision-based system able to analyze the aircraft's surroundings and to provide the pilots with a "second pair of eyes" can contribute to enhancing their safety. To this end, we develop a deep learning approach to jointly detect power line cables and pylons from images captured at distances of several hundred meters by aircraft-mounted cameras. In doing so, we combine a modern convolutional architecture with transfer learning and a loss function adapted to curvilinear structure delineation. We use a single network for both detection tasks and demonstrate its performance on two benchmarking datasets. We have also integrated it within an onboard system and run it inflight. We show with our experiments that it outperforms the prior distant cable detection method by Stambler et al. (in: International Conference on Robotics and Automation, 2019) on both datasets, while also successfully detecting pylons, given their annotations are available for the data.