Abstract In this paper Discrete Material and Thickness Optimization (DMTO) is used to optimize sandwich composite structures subject to both displacement and linear buckling constraints. Using a new thickness formulation where density design variables scale ply thicknesses rather than constitutive properties, it is possible to size both core and face sheet plies simultaneously. This makes it possible to have different ply thicknesses for core and face sheet layers while also covering ply-drops. Furthermore, separating core and face sheets allows enforcing a symmetric lay-up which can be important to avoid warping during curing. The approach is demonstrated in three numerical examples of increasing complexity.