This work introduces the use of the treed Gaussian process (TGP) as a surrogate model within the mesh adaptive direct search (MADS) framework for constrained blackbox optimization. It extends the surrogate management framework (SMF) to nonsmooth optimization under general constraints. MADS uses TGP in two ways: one, as a surrogate for blackbox evaluations, and two, to evaluate statistical criteria such as the expected improvement and the expected reduction in variance. The efficiency of the method is tested on two problems: a synthetic one with many local optima, and one real application from a chemical engineering simulator for styrene production. In both cases we show that the TGP surrogate is preferable to a quadratic model and to MADS without any surrogate at all.