Speech is a noninvasive digital phenotype that can offer valuable insights into mental health conditions, but it is often treated as a single modality. In contrast, we propose the treatment of patient speech data as a trimodal multimedia data source for depression detection. This study explores the potential of large language model-based architectures for speech-based depression prediction in a multimodal regime that integrates speech-derived text, acoustic landmarks, and vocal biomarkers. Adolescent depression presents a significant challenge and is often comorbid with multiple disorders, such as suicidal ideation and sleep disturbances. This presents an additional opportunity to integrate multi-task learning (MTL) into our study by simultaneously predicting depression, suicidal ideation, and sleep disturbances using the multimodal formulation. We also propose a longitudinal analysis strategy that models temporal changes across multiple clinical interactions, allowing for a comprehensive understanding of the conditions' progression. Our proposed approach, featuring trimodal, longitudinal MTL is evaluated on the Depression Early Warning dataset. It achieves a balanced accuracy of 70.8%, which is higher than each of the unimodal, single-task, and non-longitudinal methods.