We utilize the ensemble of trees framework, a tractable mixture over super-exponential number of tree-structured distributions, to develop a new model for multivariate density estimation. The model is based on the construction of tree-structured copulas -- multivariate distributions with uniform on [0,1] marginals. By averaging over all possible tree structures, the new model can approximate distributions with complex variable dependencies. We propose an EM algorithm to estimate the parameters for these tree-averaged models for both the real-valued and the categorical case. Based on the tree-averaged framework, we propose a new model for joint precipitation amounts data on networks of rain stations.