Ormia ochracea is a parasitoid fly known for its extremely precise sound localization abilities, which it uses to locate its preferred host, Gryllidae crickets. The model that explains these precise hearing abilities in Ormia ochracea may be the only detailed mathematical model of the mechanics of hearing in response to incident acoustic waves in a binaural organism. This model accurately predicts the interaural amplitude difference (ITD) between the tympana for all incident sound angles; however, the model fails to predict the interaural time delay (IAD) accurately for high incident sound angles. To explore the reason for this failure, we used synchrotron radiation microtomography to determine the 3D morphology of the tympana of two Ormia ochracea specimens. Previous models assume that these structures operate as 2D-like plates, but imaging reveals that the tympanal structures are complex and three-dimensional in nature. Using this new information to improve the model of hearing in Ormia ochracea, we added a term that represents the tympanum’s elastic material response in the lateral direction and recovers observed IAD for all incident sound angles. This work demonstrates that hearing in Ormia ochracea involves acoustic information and physiological responses in two primary planes, rather than one. It is possible that this improved model may be useful in the design of improved microscale auditory devices, including several insect-inspired directional microphones and hearing aids.