ABSTRACT Radio continuum emission is a dust-unbiased tracer of both thermal and non-thermal processes in the interstellar medium. We present new maps of the free–free and synchrotron emission in the Magellanic Clouds (MCs) at 0.166, 1.4, and 4.8 GHz with no prior assumption about the radio non-thermal spectrum. The maps were constructed using a de-reddened H α map as a template for the thermal radio emission, which we subtract from maps of the total radio continuum emission. To de-redden the H α emission, it is important to know the fraction of dust surface density that attenuates the H α emission along the line of sight, fd. This fraction is obtained by comparing the dust opacity obtained through the infrared emission spectrum and the Balmer decrement method. In star-forming regions, the median fd is about 0.1, which is lower than that in diffuse regions by a factor of three. We obtain a global thermal radio fraction, fth, of 30 per cent (35 per cent) in the LMC (SMC) at 1.4 GHz. Furthermore, we present maps of the equipartition magnetic field strength with average values of $\simeq \, 10.1\, \mu$G in the LMC and $\simeq \, 5.5\, \mu$G in the SMC. The magnetic field is proportional to the star-formation rate to the power of 0.24 and 0.20 for the LMC and SMC, respectively. This study shows that non-thermal processes control the interstellar medium in the MCs.