Microwave photonics offers a promising solution for frequency converting microwave signals, however, demonstrations so far have either been bulky fibre implementations or lacked rejection of interfering image signals. Here, we demonstrate the first microwave photonic mixer with image rejection of broadband signals utilising chip-based stimulated Brillouin scattering and interferometry. We demonstrate frequency down-conversion of carrier frequencies ranging from 10 GHz-16 GHz, ultra-high image rejection for a single tone of up to 70 dB, and 100 MHz and 400 MHz wide analogue signals with 28.5 dB and 16 dB image rejection, respectively. Furthermore, we down-convert 200 Mb/s quadrature-phase-shift keying signals with an error vector magnitude as low as -9.6 dB when simultaneously present interfering image signals are suppressed by the mixer.