Advanced driver assistance systems require a comprehensive understanding of the driver's mental/physical state and traffic context but existing works often neglect the potential benefits of joint learning between these tasks. This paper proposes MMTL-UniAD, a unified multi-modal multi-task learning framework that simultaneously recognizes driver behavior (e.g., looking around, talking), driver emotion (e.g., anxiety, happiness), vehicle behavior (e.g., parking, turning), and traffic context (e.g., traffic jam, traffic smooth). A key challenge is avoiding negative transfer between tasks, which can impair learning performance. To address this, we introduce two key components into the framework: one is the multi-axis region attention network to extract global context-sensitive features, and the other is the dual-branch multimodal embedding to learn multimodal embeddings from both task-shared and task-specific features. The former uses a multi-attention mechanism to extract task-relevant features, mitigating negative transfer caused by task-unrelated features. The latter employs a dual-branch structure to adaptively adjust task-shared and task-specific parameters, enhancing cross-task knowledge transfer while reducing task conflicts. We assess MMTL-UniAD on the AIDE dataset, using a series of ablation studies, and show that it outperforms state-of-the-art methods across all four tasks.