Bilateral rehabilitation allows patients with hemiparesis to exploit the cooperative capabilities of both arms to promote the recovery process. Although various approaches have been proposed to facilitate synchronized robot-assisted bilateral movements, few studies have focused on addressing the varying joint stiffness resulting from dynamic motions. This paper presents a novel bilateral rehabilitation system that implements a surface electromyography (sEMG)-based stiffness control to achieve real-time stiffness adjustment based on the user's dynamic motion. An sEMG-driven musculoskeletal model that incorporates the muscle activation and muscular contraction dynamics is developed to provide reference signals for the robot's real-time stiffness control. Preliminary experiments were conducted to evaluate the system performance in tracking accuracy and comfortability, which showed the proposed rehabilitation system with sEMG-based real-time stiffness variation achieved fast adaption to the patient's dynamic movement as well as improving the comfort in robot-assisted bilateral training.