Cancers are commonly characterized by a complex pathology encompassing genetic, microscopic and macroscopic features, which can be probed individually using imaging and omics technologies. Integrating these data to obtain a full understanding of pathology remains challenging. We introduce a method called deep latent variable path modelling, which combines the representational power of deep learning with the capacity of path modelling to identify relationships between interacting elements in a complex system. To evaluate the capabilities of deep latent variable path modelling, we initially trained a model to map dependencies between single-nucleotide variant, methylation profiles, microRNA sequencing, RNA sequencing and histological data using breast cancer data from The Cancer Genome Atlas. This method exhibited superior performance in mapping associations between data types compared with classical path modelling. We additionally performed successful applications of the model to stratify single-cell data, identify synthetic lethal interactions using CRISPR-Cas9 screens derived from cell lines and detect histologic-transcriptional associations using spatial transcriptomic data. Results from each of these data types can then be understood with reference to the same holistic model of illness.