The flow within adhering droplets subjected to external shear flows has a significant influence on the stability and eventual detachment of the droplets from the surface. Most commonly, the velocity field inside adhering droplets is measured by means of particle image velocimetry (PIV), which requires a correction step for distortion caused by refraction of light at the gas-liquid interface. Current methods for distortion correction based on ray tracing are limited to low external flow velocities. However, the ray-tracing method can be extended to arbitrarily deformed droplet shapes if the instantaneous three-dimensional droplet interface is availble. In the present work, a previously introduced method for the image-based reconstruction of gas-liquid interfaces by means of deep learning is adapted to determine the instantaneous interface of adhering droplets in external shear flows. In this regard, a purposefully developed optical measurement technique based on the shadowgraphy method is employed that encodes additional three-dimensional (3D) information of the interface in the images via glare points from lateral light sources. On the basis of the images recorded in the experiments, the volumetric shape of the droplet is reconstructed by a neural network that was trained on the spatio-temporal dynamics of the gas-liquid interface from a synthetic dataset obtained by numerical simulation. The results for experiments with adhering droplets at different velocities of external flow demonstrate that the combination of the learned droplet geometry with the depth encoding through the glare points facilitates a robust and flexible reconstruction. The proposed method reconstructs the instantaneous three-dimensional interface of adhering droplets at both high resolution and spatial accuracy and thereby enables the distortion correction of PIV measurements at high external flow velocities.