Most diffusion biophysical models capture basic properties of tissue microstructure, such as diffusivity and anisotropy. More realistic models that relate the diffusion-weighted signal to cell size and membrane permeability often require simplifying assumptions such as short gradient pulse and Gaussian phase distribution, leading to tissue features that are not necessarily quantitative. Here, we propose a method to quantify tissue microstructure without jeopardizing accuracy owing to unrealistic assumptions. Our method utilizes realistic signals simulated from the geometries of cellular microenvironments as fingerprints, which are then employed in a spherical mean estimation framework to disentangle the effects of orientation dispersion from microscopic tissue properties. We demonstrate the efficacy of microstructure fingerprinting in estimating intra-cellular, extra-cellular, and intra-soma volume fractions as well as axon radius, soma radius, and membrane permeability.