For a pneumatic teleoperation system with on/off solenoid valves, sliding-mode control laws for position and force, ensuring low switching (open/close) activity of the valves are developed. Since each pneumatic actuator has two pneumatic chambers with a total of four on/off valves, sixteen possible combinations ("operating modes") for the valves' on/off positions exist, but only seven of which are both functional and unique. While previous work has focused on 3-mode sliding-based position control of one pneumatic actuator, this paper develops the seven-mode sliding-based bilateral control of a teleoperation system comprising a pair of pneumatic actuators. The proposed bilateral sliding control schemes are experimentally validated on a pair of actuators utilizing position-position and force-position teleoperation architectures. The results demonstrate that leveraging the additional modes of operation leads to more efficient and smoother control of the pneumatic teleoperation system. It was found that viscous friction forces were crippling haptic feedback in the position-position architecture. Through the use of force sensors, the force-position architecture was able to compensate for the heavy viscous friction forces.