Neural coding through inhibitory projection pathways remains poorly understood. We analyze the transmission properties of the Purkinje cell (PC) to cerebellar nucleus (CN) pathway in a modeling study using a data set recorded in awake mice containing respiratory rate modulation. We find that inhibitory transmission from tonically active PCs can transmit a behavioral rate code with high fidelity. We parameterized the required population code in PC activity and determined that 20% of PC inputs to a full compartmental CN neuron model need to be rate-comodulated for transmission of a rate code. Rate covariance in PC inputs also accounts for the high coefficient of variation in CN spike trains, while the balance between excitation and inhibition determines spike rate and local spike train variability. Overall, our modeling study can fully account for observed spike train properties of cerebellar output in awake mice, and strongly supports rate coding in the cerebellum.