Reinforcement learning (RL) has made significant strides in legged robot control, enabling locomotion across diverse terrains and complex loco-manipulation capabilities. However, the commonly used position or velocity tracking-based objectives are agnostic to forces experienced by the robot, leading to stiff and potentially dangerous behaviors and poor control during forceful interactions. To address this limitation, we present \emph{Force-Adaptive Control via Impedance Reference Tracking} (FACET). Inspired by impedance control, we use RL to train a control policy to imitate a virtual mass-spring-damper system, allowing fine-grained control under external forces by manipulating the virtual spring. In simulation, we demonstrate that our quadruped robot achieves improved robustness to large impulses (up to 200 Ns) and exhibits controllable compliance, achieving an 80% reduction in collision impulse. The policy is deployed to a physical robot to showcase both compliance and the ability to engage with large forces by kinesthetic control and pulling payloads up to 2/3 of its weight. Further extension to a legged loco-manipulator and a humanoid shows the applicability of our method to more complex settings to enable whole-body compliance control. Project Website: https://facet.pages.dev/