Double diffusion encoding (DDE) magnetic resonance measurements of the water signal offers a unique ability to separate the effect of microscopic anisotropic diffusion in structural units of tissue from the overall macroscopic orientational distribution of cells. However, the specificity in detected microscopic anisotropy is limited as the signal is averaged over different cell types and across tissue compartments. Performing side-by-side metabolite DDE spectroscopy (DDES) and water DDES in which a wide range of b-values is used to gradually eliminate the extracellular contribution provides complementary measures from which intracellular and extracellular microscopic fractional anisotropies ($mu$FA) and diffusivities can be estimated. Metabolites are largely confined to the intracellular space and therefore provide a benchmark for intracellular diffusivity of specific cell types. Here, we aimed to estimate tissue- and compartment-specific human brain microstructure by combining water and metabolites DDES experiments. We performed DDES in human subjects in two brain regions that contain widely different amounts of white matter (WM) and gray matter (GM): parietal white matter (PWM) and occipital gray matter (OGM) on a 7 T MRI scanner. Results of the metabolite DDES experiments in both PWM and OGM suggest a highly anisotropic intracellular space within neurons and glia, with the possible exception of gray matter glia. Tortuosity values in the cytoplasm for water and tNAA, obtained with correlation analysis of microscopic parallel diffusivity with respect to GM/WM tissue fraction in the volume of interest, are remarkably similar for both molecules, while exhibiting a clear difference between gray and white matter, suggesting a more crowded cytoplasm and more complex cytomorphology of neuronal cell bodies and dendrites in GM than those found in long-range axons in WM.