Factor copula models have been recently proposed for describing the joint distribution of a large number of variables in terms of a few common latent factors. In this talk, we supplement the factor copula model with a combination of a factor copula model at the first tree level and a truncated vine copula structure at a higher tree level. The model can capture different behaviours at the tail of the distribution but also remains parsimonious with interpretable economic meanings. A Bayesian procedure is employed for fast inference in multi-factor and structured factor copulas. To deal with the high-dimensional structure, a Variational Inference (VI) algorithm is applied to estimate different specifications of factor copula models. Compared to Markov Chain Monte Carlo (MCMC) sampling, the variational approximation is much faster. The bivariate copula functions connecting the variables in factor copula models are unknown in high dimensions. An automatic procedure based on the Bayesian Information Criterion (BIC) is derived to recover the hidden dependence structure. We use the structured factor copulas to model the joint and conditional distress probabilities of banks in Europe and the United States.