Mental-health stigma remains a pervasive social problem that hampers treatment-seeking and recovery. Existing resources for training neural models to finely classify such stigma are limited, relying primarily on social-media or synthetic data without theoretical underpinnings. To remedy this gap, we present an expert-annotated, theory-informed corpus of human-chatbot interviews, comprising 4,141 snippets from 684 participants with documented socio-cultural backgrounds. Our experiments benchmark state-of-the-art neural models and empirically unpack the challenges of stigma detection. This dataset can facilitate research on computationally detecting, neutralizing, and counteracting mental-health stigma. Our corpus is openly available at https://github.com/HanMeng2004/Mental-Health-Stigma-Interview-Corpus.