Haptic upper limb exoskeletons are robots that assist human operators during task execution while having the ability to render virtual or remote environments. Therefore, the stability of such robots in physical human-robot-environment interaction must be guaranteed, in addition to performing well during task execution. Having a wide range of Z-width, which shows the region of passively renderable impedance by a haptic display, is also important to render a wide range of virtual environments. To address these issues, in this study, subsystem-based adaptive impedance control is designed for having a stable human-robot-environment interaction of 7 degrees of freedom haptic exoskeleton. The presented control decomposes the entire system into subsystems and designs the controller at the subsystem level. The stability of the controller in the presence of contact with the virtual environment and human arm force is proved by employing the virtual stability concept. Additionally, the Z-width of the 7-DoF haptic exoskeleton is drawn using experimental data and improved using varying virtual mass element for the virtual environment. Finally, experimental results are provided to demonstrate the perfect performance of the proposed controller in accomplishing the predefined task.