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 .