We consider the solution of derivative-free optimization problems with continuous, integer, discrete and categorical variables in the context of costly black-box mixed-variable industrial problems. Our approach is based on NOMAD, an implementation of the mesh-adaptive direct-search method (MADS), supplemented with surrogate models and strategies in the local poll and global search steps. The surrogate models are radial basis function interpolations managed by the surrogate-assisted evolutionary software MINAMO developed at Cenaero. The proposed approach is validated on a collection of problems from the literature and we compare several surrogate-based strategies. In the general mixed-variable case, the results show that employing MINAMO as a surrogate-based strategy within NOMAD in the poll and search steps increases both robustness and efficiency when compared to MINAMO's surrogate-based evolutionary algorithm alone or to NOMAD. On problems with mixed-integer variables only, we also experiment with the specialized mixed-integer solver BONMIN instead of MINAMO's evolutionary algorithm in the search step. It turns out to be slightly more efficient and substantially more robust when high accuracy is required.