Bimanual dexterous manipulation relies on integrating multimodal inputs to perform complex real-world tasks. To address the challenges of effectively combining these modalities, we propose DECO, a decoupled multimodal diffusion transformer that disentangles vision, proprioception, and tactile signals through specialized conditioning pathways, enabling structured and controllable integration of multimodal inputs, with a lightweight adapter for parameter-efficient injection of additional signals. Alongside DECO, we release DECO-50 dataset for bimanual dexterous manipulation with tactile sensing, consisting of 50 hours of data and over 5M frames, collected via teleoperation on real dual-arm robots. We train DECO on DECO-50 and conduct extensive real-world evaluation with over 2,000 robot rollouts. Experimental results show that DECO achieves the best performance across all tasks, with a 72.25% average success rate and a 21% improvement over the baseline. Moreover, the tactile adapter brings an additional 10.25% average success rate across all tasks and a 20% gain on complex contact-rich tasks while tuning less than 10% of the model parameters.