Hybrid Reconfigurable Intelligent Surfaces (HRISs), which are capable of simultaneous programmable reflections and sensing, are expected to play a significant role in future wireless networks, enabling various Integrated Sensing and Communication (ISAC) applications. In this paper, we focus on HRIS-enabled Unmanned Aerial Vehicle (UAV) networks and design the HRIS parameters (phase profile, reception combining, and the power splitting between the two functionalities) for jointly estimating the individual UAV-HRIS and HRIS-base-station channels as well as the Angle of Arrival (AoA) of the Line-of-Sight (LoS) component of the UAV-HRIS channel. We derive the Cramér Rao lower bounds for the estimated channels and evaluate the performance of the proposed approach in terms of the channel estimation error and the LoS AoA estimation accuracy, verifying its effectiveness for HRIS-enabled ground-to-UAV wireless communication systems.