  The radio continuum emission is a dust-unbiased tracer of both the 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 4.8GHz with no prior assumption about the radio non-thermal spectrum.
The maps were constructed using a de-reddened H$\alpha$ 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$\alpha$ emission, it is important to
know the fraction of dust surface density that attenuates the H$\alpha$
emission along the line-of-sight, $f_\text{d}$. 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 $f_\text{d}$
is about 0.1 which is by a factor of 3 lower than that in diffuse regions. We
obtain a global thermal radio fraction, $f_\text{th}$, of 30 per cent (35 per
cent) in the LMC (SMC) at 1.4GHz. Furthermore, we present maps of the
equipartition magnetic field strength with average values of $\simeq10.1\mu$G
in the LMC and $\simeq\,5.5\,\mu$G in the SMC. The magnetic field is
proportional to the star formation rate to a power of 0.24 and 0.20 for the LMC
and SMC, respectively. This study shows that the non-thermal processes control
the interstellar medium in the MCs.
