Hybrid NMR (hdNMR) is a powerful new tool that combines the strengths of solution- and solid-state NMR to measure dipolar, chemical shift, and quadrupolar tensors in aqueous solution. We introduce the theory of hdNMR and partially randomly oriented (PRO) crystalline hydrogel samples. PRO samples produce randomly oriented spectra with characteristic Pake patterns from the solid state, yet they maintain the high resolution dispersion of solution NMR experiments. With new pulse sequences, we show how hdNMR can be used to measure with high precision the H-1(alpha)-C-13(alpha) dipolar tensor and carboxylate chemical shift anisotropy tensor of aspartate. These measurements contain detailed information on the distribution of electron density, interatomic distances, and the orientation dependence of molecular motion.