Knowledge of how proteins interact with DNA is essential for understanding gene regulation. Although DNA-binding specificities for thousands of transcription factors (TFs) have been determined, the specific amino acid-base interactions comprising their structural interfaces are largely unknown. This lack of resolution hampers attempts to leverage these data in order to predict specificities for uncharacterized TFs or TFs mutated in disease. Here we introduce recognition code learning via automated mapping of protein-DNA structural interfaces (rCLAMPS), a probabilistic approach that uses DNA-binding specificities for TFs from the same structural family to simultaneously infer both which nucleotide positions are contacted by particular amino acids within the TF as well as a recognition code that relates each base-contacting amino acid to nucleotide preferences at the DNA positions it contacts. We apply rCLAMPS to homeodomains, the second largest family of TFs in metazoans and show that it learns a highly effective recognition code that can predict de novo DNA-binding specificities for TFs. Furthermore, we show that the inferred amino acid-nucleotide contacts reveal whether and how nucleotide preferences at individual binding site positions are altered by mutations within TFs. Our approach is an important step toward automatically uncovering the determinants of protein-DNA specificity from large compendia of DNA-binding specificities and inferring the altered functionalities of TFs mutated in disease.