Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously in physics, chemistry and biology. The recently developed concept of spreadability, $\mathcal{S}(t)$, provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales. To investigate the capability of $\mathcal{S}(t)$ to probe microstructures of real heterogeneous media, we explicitly compute $\mathcal{S}(t)$ for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. We further confirm that the small-, intermediate- and long-time behaviors of $\mathcal{S}(t)$ sensitively capture the small-, intermediate- and large-scale characteristics of the models. Lessons learned from such analyses of our models are used to determine accurately the large-scale structural characteristics of a sample Fontainebleau sandstone, which we show is nonhyperuniform. Our study demonstrates the practical applicability of the diffusion spreadability to extract crucial microstructural information from real data across length scales and provides a basis for the inverse design of materials with desirable time-dependent diffusion properties.