Multimodal data are prevalent across various domains, and learning robust representations of such data is paramount to enhancing generation quality and downstream task performance. To handle heterogeneity and interconnections among different modalities, recent multimodal generative models extract shared and private (modality-specific) information with two separate variables. Despite attempts to enforce disentanglement between these two variables, these methods struggle with challenging datasets where the likelihood model is insufficient. In this paper, we propose Information-disentangled Multimodal VAE (IDMVAE) to explicitly address this issue, with rigorous mutual information-based regularizations, including cross-view mutual information maximization for extracting shared variables, and a cycle-consistency style loss for redundancy removal using generative augmentations. We further introduce diffusion models to improve the capacity of latent priors. These newly proposed components are complementary to each other. Compared to existing approaches, IDMVAE shows a clean separation between shared and private information, demonstrating superior generation quality and semantic coherence on challenging datasets.