Unraveling interactions between microbial communities is of vital importance in understanding how microbes influence human health. Rich sources of microbiome data have been generated by the latest sequencing experiments,measuring microbial abundances under a variety of environmental conditions,such as at different body sites or across different time points. In this paper,we model the complexity of these data, and of the underlying dependency structure, via a Gaussian copula graphical model and we propose an efficient Bayesian structural learning procedure for inference. Heterogeneity in the data is accounted for both at the individual microbial level, via marginal distributions that are linked parametrically with external covariates, and at the dependency level, with a hierarchical prior on the graph that takes the form of a latent network model, capturing structural relatedness across multiple environments as well as dependencies of the microbial interactions from external covariates.