Microarchitectural features of opaque porous media and biological tissues are of great importance in many scientific disciplines ranging from chemistry, material sciences, and geology to biology and medicine. Noninvasive characterization of coherently organized pores is rather straightforward since conventional diffusion magnetic resonance methods can detect anisotropy on a macroscopic scale; however, it remains extremely challenging to directly infer on microarchitectural features on the microscopic scale in heterogeneous porous media and biological cells that are comprised of randomly oriented compartments, a scenario widely encountered in Nature. Here, we show that the angular bipolar double-pulsed-field-gradient (bp-d-PFG) methodology is capable of reporting on unique microarchitectural features of highly heterogeneous systems. This was demonstrated on a toluene-in-water emulsion system, quartz sand, and even biological specimens such as yeast cells and isolated gray matter. We find that in the emulsion and yeast cells systems, the angular bp-d-PFG methodology uniquely revealed nearly an image of the pore space, since it conveyed direct microarchitectural information such as compartment shape and size. In two different quartz sand specimens, the angular bp-d-PFG experiments demonstrated the presence of randomly oriented anisotropic compartments. We also obtained unequivocal evidence that diffusion in interconnected interstices is restricted and therefore non-Gaussian. In biological contexts, the angular bp-d-PFG experiments could uniquely differentiate between spherical cells and randomly oriented compartments in gray matter tissue, information that could not be obtained by conventional NMR methods. The angular bp-d-PFG methodology also performs very well even when severe background gradients are present, as is often encountered in realistic systems. We conclude that this method seems to be the method of choice for characterizing the microstructure of porous media and biological cells noninvasively.