Despite the proliferation and clinical deployment of artificial intelligence (AI)-based medical software devices, most remain black boxes that are uninterpretable to key stakeholders including patients, physicians, and even the developers of the devices. Here, we present a general model auditing framework that combines insights from medical experts with a highly expressive form of explainable AI that leverages generative models, to understand the reasoning processes of AI devices. We then apply this framework to generate the first thorough, medically interpretable picture of the reasoning processes of machine-learning-based medical image AI. In our synergistic framework, a generative model first renders "counterfactual" medical images, which in essence visually represent the reasoning process of a medical AI device, and then physicians translate these counterfactual images to medically meaningful features. As our use case, we audit five high-profile AI devices in dermatology, an area of particular interest since dermatology AI devices are beginning to achieve deployment globally. We reveal how dermatology AI devices rely both on features used by human dermatologists, such as lesional pigmentation patterns, as well as multiple, previously unreported, potentially undesirable features, such as background skin texture and image color balance. Our study also sets a precedent for the rigorous application of explainable AI to understand AI in any specialized domain and provides a means for practitioners, clinicians, and regulators to uncloak AI's powerful but previously enigmatic reasoning processes in a medically understandable way.