  We have acquired radio continuum data between 70\,MHz and 48\,GHz for a
sample of 19 southern starburst galaxies at moderate redshifts ($0.067 < z <
0.227$) with the aim of separating synchrotron and free-free emission
components. Using a Bayesian framework we find the radio continuum is rarely
characterised well by a single power law, instead often exhibiting low
frequency turnovers below 500\,MHz, steepening at mid-to-high frequencies, and
a flattening at high frequencies where free-free emission begins to dominate
over the synchrotron emission. These higher order curvature components may be
attributed to free-free absorption across multiple regions of star formation
with varying optical depths. The decomposed synchrotron and free-free emission
components in our sample of galaxies form strong correlations with the
total-infrared bolometric luminosities. Finally, we find that without
accounting for free-free absorption with turnovers between 90 to 500\,MHz the
radio-continuum at low frequency ($\nu < 200$\,MHz) could be overestimated by
upwards of a factor of twelve if a simple power law extrapolation is used from
higher frequencies. The mean synchrotron spectral index of our sample is
constrained to be $\alpha=-1.06$, which is steeper then the canonical value of
$-0.8$ for normal galaxies. We suggest this may be caused by an intrinsically
steeper cosmic ray distribution.
