This work presents a compliant and passive shared control framework for teleoperated robot-assisted tasks. Inspired by the human operator's capability of continuously regulating the arm impedance to perform contact-rich tasks, a novel control schema, exploiting the variable impedance control framework for force tracking is proposed. Moreover, bilateral teleoperation and shared control strategies are implemented to alleviate the human operator's workload. Furthermore, a global energy tank-based approach is integrated to enforce the system's passivity. The proposed framework is first evaluated to assess the force-tracking capability when the robot autonomously performs contact-rich tasks, e.g., in an ultrasound scanning scenario. Then, a validation experiment is conducted utilizing the proposed shared control framework. Finally, the system's usability is investigated with 12 users. The experiment results in system assessment revealed a maximum median error of 0.25 N across all the force-tracking experiment setups, i.e., constant and time-varying ones. Then, the validation experiment demonstrated significant improvements regarding the force tracking tasks compared to conventional control methods, and the system passivity was preserved during the task execution. Finally, the usability experiment shows that the human operator workload is significantly reduced by$54.6 \%$compared to the other two control modalities. The proposed framework holds significant potential for the execution of remote robot-assisted medical procedures, such as palpation and ultrasound scanning, particularly in addressing deformation challenges while ensuring safety, compliance, and system passivity.