Cross-domain disentanglement is the problem of learning representations partitioned into domain-invariant and domain-specific representations, which is a key to successful domain transfer or measuring semantic distance between two domains. Grounded in information theory, we cast the simultaneous learning of domain-invariant and domain-specific representations as a joint objective of multiple information constraints, which does not require adversarial training or gradient reversal layers. We derive a tractable bound of the objective and propose a generative model named Interaction Information Auto-Encoder (IIAE). Our approach reveals insights on the desirable representation for cross-domain disentanglement and its connection to Variational Auto-Encoder (VAE). We demonstrate the validity of our model in the image-to-image translation and the cross-domain retrieval tasks. We further show that our model achieves the state-of-the-art performance in the zero-shot sketch based image retrieval task, even without external knowledge.