We present the discovery of NGTS-3Ab, a hot Jupiter found transiting the primary star of an unresolved binary system. We develop a joint analysis of multi-colour photometry, centroids, radial velocity (RV) cross-correlation function (CCF) profiles and their bisector inverse slopes (BIS) to disentangle this three-body system. Data from the Next Generation Transit Survey (NGTS), SPECULOOS and HARPS are analysed and modelled with our new blendfitter software. We find that the binary consists of NGTS-3A (G6V-dwarf) and NGTS-3B (K1V-dwarf) at <1 arcsec separation. NGTS-3Ab orbits every P = 1.675 days. The planet radius and mass are R_planet = 1.48+-0.37 R_J and M_planet = 2.38+-0.26 M_J, suggesting it is potentially inflated. We emphasise that only combining all the information from multi-colour photometry, centroids and RV CCF profiles can resolve systems like NGTS-3. Such systems cannot be disentangled from single-colour photometry and RV measurements alone. Importantly, the presence of a BIS correlation indicates a blend scenario, but is not sufficient to determine which star is orbited by the third body. Moreover, even if no BIS correlation is detected, a blend scenario cannot be ruled out without further information. The choice of methodology for calculating the BIS can influence the measured significance of its correlation. The presented findings are crucial to consider for wide-field transit surveys, which require wide CCD pixels (>5 arcsec) and are prone to contamination by blended objects. With TESS on the horizon, it is pivotal for the candidate vetting to incorporate all available follow-up information from multi-colour photometry and RV CCF profiles.