Many translucent materials consist of evenly-distributed heterogeneous elements which produce a complex appearance under different lighting and viewing directions. For these quasi-homogeneous materials, existing techniques do not address how to acquire their material representations from physical samples in a way that allows arbitrary geometry models to be rendered with these materials. We propose a model for such materials that can be readily acquired from physical samples. This material model can be applied to geometric models of arbitrary shapes, and the resulting objects can be efficiently rendered without expensive subsurface light transport simulation. In developing a material model with these attributes, we capitalize on a key observation about the subsurface scattering characteristics of quasi-homogeneous materials at different scales. Locally, the non-uniformity of these materials leads to inhomogeneous subsurface scattering. For subsurface scattering on a global scale, we show that a lengthy photon path through an even distribution of heterogeneous elements statistically resembles scattering in a homogeneous medium. This observation allows us to represent and measure the global light transport within quasi-homogeneous materials as well as the transfer of light into and out of a material volume through surface mesostructures. We demonstrate our technique with results for several challenging materials that exhibit sophisticated appearance features such as transmission of back illumination through surface mesostructures.