The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction φ_p increases. The suspensions jam - and therefore drainage stops - for values φ_p^* which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that φ_p^* accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of the suspension - from flow to jamming - by taking into account explicitly the divergence of its effective viscosity at φ_p^*. Beyond the scope of drainage, the reported jamming transition is expected to have a deep significance for all aspects related to particulate foams, from aging to mechanical properties.