We investigate the drainage behaviour of foamy granular suspensions. Results reveal large fluctuations in the drainage velocity as bubble size, particle size and gas volume fraction are varied for a given particle volume fraction. Particle capture is proved to control the overall drainage behaviour through the parameter lambda, which compares the particle size to the size of passage through constrictions within the foam pore space. lambda highlights a sharp transition: for lambda < 1 particles are free to drain with the liquid, which involves the shear of the suspension in foam interstices, for lambda > 1 particles are trapped and the resulting drainage velocity is strongly reduced. A phenomenological model is proposed to describe this behaviour.