We study the consequences of drying on the internal structure of compressible materials containing pores of different sizes, which may be seen as model systems of sponges or wood. With the help of original techniques, we devise biporous media with different relative amounts of small and large pores, and follow the evolution of the liquid fraction simultaneously in each pore type. We show that in a compressible biporous medium with dispersed large pores (i.e., not directly connected) drying induces the homogeneous emptying of the large pores first, due to their compression, along with some compression of the small-pore matrix. In contrast, when the large pores are connected, they successively empty without compression. In both cases, the small pores start or finish to empty in the next stage, and a constant drying rate is observed during most of the time, thanks to liquid films maintaining the contact of the liquid network with the free surface of the sample.