Pure rotational spectra of (MgH)-Mg-25 (X-2 Sigma(+)) and (ZnH)-Zn-67 (X-2 Sigma(+)) were recorded using direct absorption techniques These free radicals were synthesized by the reaction of metal vapor, generated in a Broida-type oven, with H-2 in a dc discharge. The N = 0 -> 1 and N = 1 -> 2 transitions were recorded for both species in the frequency range 342-789 GHz. Spin-rotation and metal and proton hyperfine interactions were resolved in the spectra. From these data, rotational, fine structure, and hyperfine constants were determined, including the Fermi contact, dipolar, and electric quadrupole parameters of the Mg-25 and Zn-67 nuclei. Comparison of the metal and proton hyperfine terms suggests that the unpaired electron resides in a sigma molecular orbital that has significant s contributions from both the metal and the hydrogen atoms. The dipolar terms for both metals are relatively large, in contrast to those of the proton, and indicate sp sigma and possibly sd sigma (zinc only) orbital hybridization. The quadrupole constants arise principally from the p/d orbital character of the unpaired electron, although there is a non negligible polarization contribution. These results suggest significant covalent character in both MgH and ZnH, in contrast to their fluoride analogs.