For an individual suffering from a neurological condition, such as spinal cord injury, traumatic brain injury, or stroke, motorized functional electrical stimulation (FES) cycling is a rehabilitation strategy, which offers numerous health benefits. Motorized FES cycling is an example of physical human-robot interaction in which both systems must be controlled; the human is actuated by applying neuromuscular electrical stimulation to the large leg muscle groups, and the cycle is actuated through its onboard electric motor. While the rider is stimulated using a robust sliding-mode controller, the cycle utilizes an admittance controller to preserve rider safety. The admittance controller is shown to be passive with respect to the rider, and the cadence controller is shown to be globally exponentially stable through a Lyapunov-like switched systems stability analysis. Experiments are conducted on three able-bodied participants and four participants with neurological conditions (NCs) to demonstrate the efficacy of the developed controller and investigate the effect of manipulating individual admittance parameters. Results demonstrate an average admittance cadence error of -0.06±1.47 RPM for able-bodied participants and -0.02 ± 0.93 RPM for participants with NCs.