The aim of this study is to demonstrate how the logarithmic millimeter continuum gradient observed using the Atacama Large Millimeter/submillimeter Array (ALMA) may be used to estimate optical thickness in the solar atmosphere. We discuss how using multiwavelength millimeter measurements can refine plasma analysis through knowledge of the absorption mechanisms. Here we use subband observations from the publicly available science verification (SV) data, while our methodology will also be applicable to regular ALMA data. The spectral resolving capacity of ALMA SV data is tested using the enhancement coincident with an X-ray bright point and from a plasmoid ejection event near active region NOAA12470 observed in Band 3 (84–116 GHz) on 2015 December 17. We compute the interferometric brightness temperature light curve for both features at each of the four constituent subbands to find the logarithmic millimeter spectrum. We compared the observed logarithmic spectral gradient with the derived relationship with optical thickness for an isothermal plasma to estimate the structures' optical thicknesses. We conclude, within 90% confidence, that the stationary enhancement has an optical thickness between 0.02 ≤ τ ≤ 2.78, and that the moving enhancement has 0.11 ≤ τ ≤ 2.78, thus both lie near to the transition between optically thin and thick plasma at 100 GHz. From these estimates, isothermal plasmas with typical Band 3 background brightness temperatures would be expected to have electron temperatures of ~7370–15300 K for the stationary enhancement and between ~7440 and 9560 K for the moving enhancement, thus demonstrating the benefit of subband ALMA spectral analysis.