Recent advances in visuomotor policy learning have enabled robots to perform control directly from visual inputs. Yet, extending such end-to-end learning from single-arm to bimanual manipulation remains challenging due to the need for both independent perception and coordinated interaction between arms. Existing methods typically favor one side -- either decoupling the two arms to avoid interference or enforcing strong cross-arm coupling for coordination -- thus lacking a unified treatment. We propose CUBic, a Coordinated and Unified framework for Bimanual perception and control that reformulates bimanual coordination as a unified perceptual modeling problem. CUBic learns a shared tokenized representation bridging perception and control, where independence and coordination emerge intrinsically from structure rather than from hand-crafted coupling. Our approach integrates three components: unidirectional perception aggregation, bidirectional perception coordination through two codebooks with shared mapping, and a unified perception-to-control diffusion policy. Extensive experiments on the RoboTwin benchmark show that CUBic consistently surpasses standard baselines, achieving marked improvements in coordination accuracy and task success rates over state-of-the-art visuomotor baselines.