Recent advancements in multimodal Variational AutoEncoders (VAEs) have highlighted their potential for modeling complex data from multiple modalities. However, many existing approaches use relatively straightforward aggregating schemes that may not fully capture the complex dynamics present between different modalities. This work introduces a novel multimodal VAE that incorporates a Markov Random Field (MRF) into both the prior and posterior distributions. This integration aims to capture complex intermodal interactions more effectively. Unlike previous models, our approach is specifically designed to model and leverage the intricacies of these relationships, enabling a more faithful representation of multimodal data. Our experiments demonstrate that our model performs competitively on the standard PolyMNIST dataset and shows superior performance in managing complex intermodal dependencies in a specially designed synthetic dataset, intended to test intricate relationships.