We have obtained simultaneous high resolution H alpha and Na I D spectra of five dwarf M stars that span a wide range in chromospheric activity level. The observed Na I D lines exhibit behavior that is qualitatively similar to that of more well established diagnostics such as the CaII HK lines: as the activity level, as indicated by the H alpha line, increases, the absorption core brightens and then develops an emission reversal. We compare the observed profiles with computed non-LTE profiles from a grid of chromospheric/transistion region models. We find that the H alpha and the Na I D lines tend to be in general agreement as indicators of approximate chromospheric activity level. However, the H alpha line systematically indicates a value for the mass loading at the onset of the Transition Region and the location of T_min that is 0.4 dex lower in column mass density than that indicated by NaI D. Therefore, the profile of both lines cannot be simultaneously well fit for all but one of our stars. We also find, in agreement with the pioneering study of Andretta et al. (1997), that for dMe stars the shape of the Na I D emission is a much more sensitive indicator of chromospheric thickness (or, equivalently, chromospheric steepness) than is H alpha, and, therefore, provides a powerful diagnostic complement to H alpha. Finally, we investigate the dependence of the predicted line profiles on the values of the stellar parameters and conclude that the inferred chromospheric pressure is sensitive to the choice of T_eff and log g, especially among dMe stars. Specifically, among dMe stars, a model in which the value of T_eff is too small or too large by approximately 200 K, or in which the value of log g is too large or too small by 0.5 dex, will give rise to closest fit values of the column mass density at the location of the Transition REgion and T_min that are too small or too large, respectively, by approximately 0.3 dex. As a result, discrepancies between the stellar parameters of our photospheric model and those of the program objects allow us to extract only upper or lower limits for the values of the column mass density at critical points in the chromospheric structure.