We present a comprehensive multifrequency catalogue of radio sources behind the Large Magellanic Cloud (LMC) between 0.2 and 20 GHz, gathered from a combination of new and legacy radio continuum surveys. This catalogue covers an area of similar to 144 deg(2) at angular resolutions from 45 arcsec to similar to 3 arcmin. We find 6434 discrete radio sources in total, of which 3789 are detected at two or more radio frequencies. We estimate the median spectral index (alpha; where S-v similar to nu(alpha)) of alpha = -0.89 and mean of -0.88 +/- 0.48 for 3636 sources detected exclusively at two frequencies (0.843 and 1.384 GHz) with similar resolution [full width at half-maximum (FWHM) similar to 40-45 arcsec]. The large frequency range of the surveys makes it an effective tool to investigate Gigahertz Peak Spectrum (GPS), Compact Steep Spectrum (CSS), and Infrared Faint Radio Source (IFRS) populations within our sample. We find 10 GPS candidates with peak frequencies near 5 GHz, from which we estimate their linear size. 1866 sources from our catalogue are CSS candidates with alpha < -0.8. We found six candidates for High Frequency Peaker (HFP) sources, whose radio fluxes peak above 5 GHz and no sources with unconstrained peaks and alpha > 0.5. We found optical counterparts for 343 of the radio continuum sources, of which 128 have a redshift measurement. Finally, we investigate the population of 123 IFRSs found in this study.