We propose a novel and versatile computational approach, based on hierarchical COSFIRE filters, that addresses the challenge of explainable retina and palmprint recognition for automatic person identification. Unlike traditional systems that treat these biometrics separately, our method offers a unified solution, leveraging COSFIRE filters’ trainable nature for enhanced selectivity and robustness, while exhibiting explainability and resilience to decision-based black-box adversarial attack and partial matching. COSFIRE filters are trainable, in that their selectivity can be determined with a one-shot learning step. In practice, we configure a COSFIRE filter that is selective for the mutual spatial arrangement of a set of automatically selected keypoints of each retina or palmprint reference image. A query image is then processed by all COSFIRE filters and it is classified with the reference image that was used to configure the COSFIRE filter that gives the strongest similarity score. Our approach, tested on the VARIA and RIDB retina datasets and the IITD palmprint dataset, achieved state-of-the-art results, including perfect classification for retina datasets and a 97.54% accuracy for the palmprint dataset. It proved robust in partial matching tests, achieving over 94% accuracy with 80% image visibility and over 97% with 90% visibility, demonstrating effectiveness with incomplete biometric data. Furthermore, while effectively resisting a decision-based black-box adversarial attack and impervious to imperceptible adversarial images, it is only susceptible to highly perceptible adversarial images with severe noise, which pose minimal concern as they can be easily detected through histogram analysis in preprocessing. In principle, the proposed learning-free hierarchical COSFIRE filters are applicable to any application that requires the identification of certain spatial arrangements of moderately complex features, such as bifurcations and crossovers. Moreover, the selectivity of COSFIRE filters is highly intuitive; and therefore, they provide an explainable solution.