This article presents an offline method for aligning an audio signal to individual instrumental parts constituting a musical score. The proposed method is based on fitting multiple hidden semi-Markov models (HSMMs) to the observed audio signal. The emission probability of each state of the HSMM is described using latent harmonic allocation (LHA), a Bayesian model of a harmonic sound mixture. Each HSMM corresponds to one musical instrument’s part, and the state duration probability is conditioned on a linear dynamics system (LDS) tempo model. Variational Bayesian inference is used to jointly infer LHA, HSMM, and the LDS. We evaluate the capability of the method to align musical audio to its score, under reverberation, structural variations, and fluctuations in onset timing among different parts.