Biomedical research is increasingly emphasizing the emerging role of multi-source big data. An example comes from electronically available records of patients from a mix of genotypic, phenotypic, multi-omic and clinical conditions. These data are, in part, already publicly available, and thus call for integration first, and modelling afterwards. Consequently, a new paradigm of data-intensive biomedicine is naturally leading to novel inference tools, dealing in particular with complex diseases and comorbidities. The latter arise when multiple diseases occur in the same patient, and the complexity of treating such cases is especially high as it involves uncertainty in diagnosis and treatment. We first review some characteristics of such multifaceted complexity, emphasizing the implications for the computational analysis of data interrelationships which in comorbidity studies necessarily span much more than correlative associations. We then describe topics that require closer attention in perspective, in view of a better understanding of the role of multi-evidenced comorbidity data. We finally suggest the rationale for using networks and their tree configurations to explore causality, thus approaching a novel synergistic and translational inference design.