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We report on our observing program⁴This paper is based on observations obtained with the Apache Point Observatory 3.5 m telescope, which is owned and operated by the Astrophysical Research Consortium. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. to capture simultaneous spectra of Ca II and Balmer lines in a sample of nearby M3 dwarfs. Our goal is to investigate the chromospheric temperature structure required to produce these lines at the observed levels. We find a strong positive correlation between instantaneous measurements of Ca II K and the Balmer lines in active stars, although these lines may not be positively correlated in time-resolved measurements. The relationship between Hα and Ca II K remains ambiguous for weak and intermediate activity stars, with Hα absorption corresponding to a range of Ca II K emission. A similar relationship is also observed between Ca II K and the higher-order Balmer lines. As our sample consists of a single spectral type, correlations between these important chromospheric tracers cannot be ascribed to continuum effects, as suggested by other authors. These data confirm prior nonsimultaneous observations of the Hα line behavior with increasing activity, showing an initial increase in the Hα absorption with increasing Ca II K emission, prior to Hα filling in and eventually becoming a pure emission line in the most active stars. We also compare our optical measurements with archival UV and X-ray measurements, finding a positive correlation between the chromospheric and coronal emission for both high and intermediate activity stars. We compare our results with previous determinations of the active fraction of low-mass stars, and discuss them in the context of surface inhomogeneity. Lastly, we discuss the application of these data as empirical constraints on new static models of quiescent M dwarf atmospheres.