Wearable sensor technologies and deep learning are transforming healthcare management. Yet, most health sensing studies focus narrowly on physical chronic diseases. This overlooks the critical need for joint assessment of comorbid physical chronic diseases and depression, which is essential for collaborative chronic care. We conceptualize multi-disease assessment, including both physical diseases and depression, as a multi-task learning (MTL) problem, where each disease assessment is modeled as a task. This joint formulation leverages inter-disease relationships to improve accuracy, but it also introduces the challenge of double heterogeneity: chronic diseases differ in their manifestation (disease heterogeneity), and patients with the same disease show varied patterns (patient heterogeneity). To address these issues, we first adopt existing techniques and propose a base method. Given the limitations of the base method, we further propose an Advanced Double Heterogeneity-based Multi-Task Learning (ADH-MTL) method that improves the base method through three innovations: (1) group-level modeling to support new patient predictions, (2) a decomposition strategy to reduce model complexity, and (3) a Bayesian network that explicitly captures dependencies while balancing similarities and differences across model components. Empirical evaluations on real-world wearable sensor data demonstrate that ADH-MTL significantly outperforms existing baselines, and each of its innovations is shown to be effective. This study contributes to health information systems by offering a computational solution for integrated physical and mental healthcare and provides design principles for advancing collaborative chronic disease management across the pre-treatment, treatment, and post-treatment phases.