For some applications involving liquid foams, such as soil remediation for example, the liquid relative permeability of the foam-filled porous medium is a crucial parameter as it sets the liquid flow rate at which active substances or nutrients (for bacteria) can be delivered deep into the medium. We are interested in the liquid relative permeability of foam-filled porous media, within the range of low liquid saturations, i.e., ≲ 20 vol % . We fill porous media (packed spherical grains) with different foams made from either alkyl polyglucosides (APG) or saponin, in such a manner that we obtain highly controlled samples in terms of the bubble-to-grain size ratio r and the liquid saturation. The liquid relative permeability of saponin samples exhibits an optimal value as a function of r, while it increases significantly for APG foams. The ratio of their relative permeability of APG/saponin reveals two regimes as a function of r: for r ≲ 0.25, the permeability ratio is equal to the ratio corresponding to the bulk foams, while for larger r values, the permeability ratio is increased by one order of magnitude. The foam microstructure changes a lot as the bubble-to-grain size ratio increases up to 0.5, so that a new liquid network is activated, made of surface channels and liquid bridges, the former connecting the latter even at low liquid saturation. These new liquid elements may greatly benefit foams with mobile interfaces such as APGs. One such issue would deserve a dedicated study to be elucidated.