In the past few years, the ALMA radio telescope has become available for solar observations. ALMA diagnostics of the solar atmosphere are of high interest because of the theoretically expected linear relationship between the brightness temperature at millimeter wavelengths and the local gas temperature in the solar atmosphere. Key for the interpretation of solar ALMA observations is understanding where in the solar atmosphere the ALMA emission originates. Recent theoretical studies have suggested that ALMA bands at 1.2 (band 6) and 3 mm (band 3) form in the middle and upper chromosphere at significantly different heights. We study the formation of ALMA diagnostics using a 2.5D radiative MHD model that includes the effects of ion-neutral interactions (ambipolar diffusion) and nonequilibrium ionization of hydrogen and helium. Our results suggest that in active regions and network regions, observations at both wavelengths most often originate from similar heights in the upper chromosphere, contrary to previous results. Nonequilibrium ionization increases the opacity in the chromosphere so that ALMA mostly observes spicules and fibrils along the canopy fields. We combine these modeling results with observations from IRIS, SDO, and ALMA to suggest a new interpretation for the recently reported dark chromospheric holes, regions of very low temperatures in the chromosphere.