Studies of the thermal structure of the solar chromosphere are typically hampered by the complexities of non-LTE radiative transfer. This issue can be addressed using observations of the millimeter continuum, which directly probes the electron temperatures in the chromosphere. In recent years, the Atacama Large Millimeter/submillimeter Array (ALMA) has made it possible, for the first time, to obtain millimeter observations of sufficient spatial resolution to supplement spectral line observations and inversions. Here, we present observations of a plage in the 3.0 mm and 1.2 mm continua with ~2 arcsecond resolution, combined with simultaneous imaging spectroscopy observations from the Interferometric Bidimensional Spectrometer (IBIS) at the Dunn Solar Telescope. We compare the observed ALMA brightness temperatures with temperatures inferred from spectral inversions using the Na D1 5896 Å and Ca II 8542 Å lines, and investigate the wide range of physical heights probed by the millimeter continuum. We find that the millimeter emission arises from a range of heights both above and below the chromospheric calcium line, depending on the local temperature profile and electron densities.