Robots are often required to interact with surrounding environments to complete specific tasks. In these scenarios the robot must behave in a stable manner in both free-space motion as well as constrained motion during the interaction. Additionally, for many of these cases it is important to track a setpoint force to complete a task or provide safe interaction in the absence of typically expensive force sensors. This force tracking is fairly straightforward using impedance control if the environment is known exactly a priori. However, in practice the environment is unlikely to be known and force tracking becomes inaccurate. To overcome this problem we present an adaptive impedance controller with adaptation laws for the environment parameters derived directly from Lyapunov-based stability analysis. This work focuses on interactions with soft environments which are represented using a non-linear, viscoelastic Hunt-Crossley model. After derivation and stability analysis of the controller, we present simulations of a 1 degree of freedom (DOF) robot interacting with two distinct soft environments to demonstrate the efficacy of the controller.