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We present observations of a solar plage in the millimeter-continuum with the ALMA and in the Ca 8542 and Na 5896 spectral lines with the Interferometric BIdimensional Spectrometer (IBIS). Our goal is to compare the measurement of local gas temperatures provided by ALMA with the temperature diagnostics provided by non-LTE inversions using STIC. In performing these inversions, we find that using column mass as the reference height scale, rather than optical depth, provides more reliable atmospheric profiles above the temperature minimum and that the treatment of non- LTE hydrogen ionization brings the inferred chromospheric temperatures into better agreement with the ALMA measurements. The Band 3 brightness temperatures are higher but well correlated with the inversion-derived temperatures at the height of formation of the Ca 8542 line core. The Band 6 temperatures instead do not show good correlations with the temperatures at any specific layer in the inverted atmospheres. We then performed inversions that included the millimeter continuum intensities as an additional constraint. Incorporating Band 3 generally resulted in atmospheres showing a strong temperature rise in the upper atmosphere, while including Band 6 led to significant regions of anomalously low temperatures at chromospheric heights. This is consistent with the idea that the Band 6 emission can come from a range of heights. The poor constraints on the chromospheric electron density with existing inversion codes introduces difficulties in determining the height(s) of formation of the millimeter continuum as well as uncertainties in the temperatures derived from the spectral lines.