We have used electron energy loss spectrometry (EELS) in the transmission electron microscope to investigate and characterize the structure of very fine-grained diamonds of interstellar origin which have been extracted from the carbonaceous meteorites Murray and Allende by severe oxidation and acid dissolution treatments. It has been shown that, compared to solar abundances, the Xe carried in these diamonds is enriched as much as twofold in p- or r-process isotopes, nitrogen is depleted 30% in 15N and hydrogen is enriched as much as 18% in deuterium. These isotopic variations reflect the stellar sources and presumably also (for the D enrichments) the effects of ion-molecule reactions in interstellar space. Our EELS results confirm a previous observation of 1s → π* ionization edge spectral features in acid dissolution residues containing interstellar diamonds and further show that the residues have a peculiar low-energy loss inelastic scattering spectrum compared to that of ordinary fee diamond: the interstellar diamond plasmon peaks are much broader, shifted down 5 eV in energy, and have fewer features than for fee diamond. We briefy review the theory of composite dielectrics and show how dynamic effective medium theory (DEMT) can be used to successfully model the meteorite diamond residues as mixtures of diamond and π-bonded carbons, using the EELS spectra of these endmembers. The best fits to the meteorite electron energy loss data are given by a mixture of diamond and hydrogenated amorphous carbon (a-C:H) having about 0.46 volume fraction of diamond. A simpler application of DEMT, in which the valence electron-atomic core interactions are treated as Lorentz oscillators, gives a poorer fit to the data and lower value for the diamond fraction in all cases. On the assumption that there are only diamond surface and volume reservoirs of carbon atoms in the meteorite residues and that the hydrogen measured in this material is present only on the diamond surfaces, the DEMT results allow us to predict an average size for the interstellar diamonds. Within analytical error, the result is in agreement with a previously determined mass-weighted mean diameter of 16 Å. We conclude that the observations and the results of the DEMT calculations are quantitatively consistent with the idea that the only important C-bearing phase in the meteorite residues is fee diamond, and that the π-bonded component is none other than the hydrogen-rich surfaces of the extremely small diamond particles. The peculiar spectral features of the interstellar diamonds thus appear to arise as the result of their unusually small size and consequently large specific surface area. Other physical properties, and hence the potential for observing them astronomically, may also be affected by the small diamond size. A corollary of these conclusions is that the isotopic anomalies observed in the meteorite diamond residues are from the diamond particles themselves and not from any additional π-bonded carbon phase of interstellar origin.