Risk assessment for climate-sensitive systems often relies on the analysis of several variables measured at many sites. In probabilistic terms, the task is to model the joint distribution of several spatially-distributed variables, and how it varies in time. This paper describes a Bayesian hierarchical framework for this purpose. Each variable follows a distribution with parameters varying in both space and time. Temporal variability is modelled by means of hidden climate indices (HCIs) that are extracted from observed variables. This is to be contrasted with the usual approach using predefined standard climate indices (SCIs) for this purpose. In the second level of the model, the HCIs and their effects are assumed to follow temporal and spatial Gaussian processes, respectively. Both inter-variable and inter-site dependences are induced by the strong effect of common HCIs. The flexibility of the framework is illustrated with a case study in Southeast Australia aimed at modeling ‘hot and dry’ summer conditions. It involves three physical variables (streamflow, precipitation and temperature) measured on three distinct station networks, with varying data availability and representing hundreds of sites in total. The HCI model delivers reliable and sharp time-varying distributions for individual variables and sites. In addition, it adequately reproduces inter-variable and inter-site dependences, whereas a corresponding SCI model (where hidden climate indices are replaced with standard ones) strongly underestimate them. It is finally suggested that HCI models may be used as downscaling tools to estimate the joint distribution of several variables at many stations from climate models or reanalyses.