A numerical method is proposed to simulate the propagation of transient poroelastic waves across heterogeneous media, in the low frequency range. A velocity-stress formulation of Biot's equations is followed, leading to a first-order differential system. This system is splitted in two parts: a propagative one discretized by a fourth-order ADER scheme, and a diffusive one that can be solved analytically. Near acoustic sources and media interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the diffusive slow compressional wave. Lastly, since the physical parameters are non-homogeneous, an immersed interface method is implemented to accurately model the jump con- ditions between the different media. The resulting method allows to investigate the propagation through porous/porous or fluid/porous media with realistic values of physical parameters. Numerical experiments in two and three dimensions and comparisons with exact solutions confirm that the whole set of compressional and shear waves is efficiently modeled.