Further innovations in bio-inspired engineering based on biosonar systems, such as bats, may arise from more detailed understanding of the underlying acoustic processes. This includes the range-dependent properties of bat heads and ears, particularly at the higher frequencies of bat vocalizations. In a companion paper Kim et al (2012 Bioinspir. Biomim.), range-dependent head-related transfer functions of a bat head cast were investigated up to 100 kHz at either ear (i.e. monaural features). The current paper extends this to consider range-dependent spectral and temporal disparities between the two ears (i.e. binaural features), using experimental data and a spherical model of a bat head to provide insights into the physical basis for these features. It was found that binaural temporal and high-frequency binaural spectral features are approximately independent of distance, having the effect of decreasing their angular resolution at close range. In contrast, low-frequency binaural spectral features are strongly distance-dependent, such that angular sensitivity can be maintained by lowering the frequency of the echolocation emission at close range. Together with the companion paper Kim et al, we speculate that distance-dependent low-frequency monaural and binaural features at short range might help explain why some species of bats that drop the frequency of their calls on target approach while approaching a target. This also provides an impetus for the design of effective emissions in sonar engineering applied to similar tasks.