HD 156424 (B2 V) is a little-studied magnetic hot star in the Sco OB4 association, previously noted to display both high-frequency radial velocity (RV) variability and magnetospheric H$alpha$ emission. We have analysed the TESS light curve, and find that it is a $beta$ Cep pulsator with 11 detectable frequencies, 4 of which are independent $p$-modes. The strongest frequency is also detectable in RVs from ground-based high-resolution spectroscopy. RVs also show a long-term variation, suggestive of orbital motion with a period of $sim$years; significant differences in the frequencies determined from TESS and RV datasets are consistent with a light-time effect from orbital motion. Close examination of the stars spectrum reveals the presence of a spectroscopic companion, however as its RV is not variable it cannot be responsible for the orbital motion and we therefore infer that the system is a hierarchical triple with a so-far undetected third star. Reanalysis of LSD profiles from ESPaDOnS and HARPSpol spectropolarimetry reveals the surprising presence of a strong magnetic field in the companion star, with $langle B_z rangle$ about $+1.5$ kG as compared to $langle B_z rangle sim -0.8$ kG for the primary. HD 156424 is thus the second hot binary with two magnetic stars. We are unable to identify a rotational period for HD 156424A. The magnetospheric H$alpha$ emission appears to originate around HD 156424B. Using H$alpha$, as well as other variable spectral lines, we determine a period of about 0.52 d, making HD 156424B one of the most rapidly rotating magnetic hot stars.
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