In many applications of absorbing structures it is important to understand their spatial response to incident fields, for example in thermal solar panels, bolometric imaging, and controlling radiative heat transfer. In practice, the illuminating field often originates from thermal sources and is only partially spatially coherent when it reaches the absorbing device. In this paper, we present a method to fully characterize the way a structure can absorb such partially coherent fields. The method is presented for any three-dimensional material and accounts for the partial coherence and partial polarization of the incident light. This characterization can be achieved numerically using simulation results or experimentally using the energy absorption interferometry that has been described previously in the literature. The absorbing structure is characterized through a set of absorbing functions onto which any partially coherent field can be projected. This set is compact for any structure of finite extent, and the absorbing function is discrete for periodic structures.