Cosmic rays (CRs) and magnetic fields are dynamically important components in the Galaxy, and their energy densities are comparable to that of the turbulent interstellar gas. The interaction of CRs and Galactic magnetic fields (GMF) produces synchrotron radiation clearly visible in the radio regime. Detailed measurements of synchrotron radiation averaged over the line-of-sight (LOS), so-called synchrotron emissivities, can be used as a tracer of the CR density and GMF strength. Our aim is to model the synchrotron emissivity in the Milky Way using a three-dimensional dataset instead of LOS-integrated intensity maps on the sky. Using absorbed HII regions, we measured the synchrotron emissivity over a part of the LOS through the Galaxy, changing from a two-dimensional to a three-dimensional view. Performing these measurements on a large scale is one of the new applications of the window opened by current low-frequency arrays. Using various simple axisymmetric emissivity models and a number of GMF-based emissivity models, we were able to simulate the synchrotron emissivities and compare them to the observed values in the catalog. We present a catalog of low-frequency absorption measurements of HII regions, their distances and electron temperatures, compiled from literature. These data show that the axisymmetric emissivity models are not complex enough, but the GMF-based emissivity models deliver a reasonable fit. These models suggest that the fit can be improved by either an enhanced synchrotron emissivity in the outer reaches of the Milky Way or an emissivity drop near the Galactic center. Current GMF models plus a constant CR density model cannot explain low-frequency absorption measurements, but the fits improved with slight (ad hoc) adaptations. It is clear that more detailed models are needed, but the current results are very promising.