Multimodal sensory data resembles the form of information perceived by humans for learning, and are easy to obtain in large quantities. Compared to unimodal data, synchronization of concepts between modalities in such data provides supervision for disentangling the underlying explanatory factors of each modality. Previous work leveraging multimodal data has mainly focused on retaining only the modality-invariant factors while discarding the rest. In this paper, we present a partitioned variational autoencoder (PVAE) and several training objectives to learn disentangled representations, which encode not only the shared factors, but also modality-dependent ones, into separate latent variables. Specifically, PVAE integrates a variational inference framework and a multimodal generative model that partitions the explanatory factors and conditions only on the relevant subset of them for generation. We evaluate our model on two parallel speech/image datasets, and demonstrate its ability to learn disentangled representations by qualitatively exploring within-modality and cross-modality conditional generation with semantics and styles specified by examples. For quantitative analysis, we evaluate the classification accuracy of automatically discovered semantic units. Our PVAE can achieve over 99% accuracy on both modalities.