Foam-based materials are promising micro-structured materials with interesting thermal and acoustical properties. The control of the material morphology requires counteracting all the destabilizing mechanisms during their production, starting with the drainage process, which remains to be understood in the case of the complex fluids that are commonly used to be foamed. Here we perform measurements for the drainage velocity of aqueous foams made with granular suspensions of hydrophilic monodisperse particles and we show that the effect of particles can be accounted by two parameters: the volume fraction of particles in the suspension (φ_p) and the confinement parameter (λ), that compares the particle size to the size of passage through constrictions in the foam network. We report data over wide ranges for those two parameters and we identify all the regimes and transitions occurring in the φ_p-λ diagram. In particular, we highlight a transition which refers to the included / excluded configuration of the particles with respect to the foam network, and makes the drainage velocity evolve from its minimal value (fully included particles) to its maximal one (fully excluded particles). We also determine the conditions (φ_p,λ) leading to the arrest of the drainage process.