Accurately diagnosing depression is difficult– requiring time-intensive interviews, assessments, and analysis. Hence, automated methods that can assess linguistic patterns in these interviews could help psychiatric professionals make faster, more informed decisions about diagnosis. We propose JLPC, a model that analyzes interview transcripts to identify depression while jointly categorizing interview prompts into latent categories. This latent categorization allows the model to define high-level conversational contexts that influence patterns of language in depressed individuals. We show that the proposed model not only outperforms competitive baselines, but that its latent prompt categories provide psycholinguistic insights about depression.