Interactions between a supermassive black hole binary and the surrounding accretion disc can both assist the binary inspiral and align the black hole spins to the disc angular momentum. While binary migration is due to angular-momentum transfer within the circumbinary disc, the spin-alignment process is driven by the mass accreting on to each black hole. Mass transfer between different disc components thus couples the inspiral and the alignment process together. Mass is expected to leak through the cavity cleared by the binary, and preferentially accretes on to the lighter (secondary) black hole which orbits closer to the disc edge. Low accretion rate on to the heavier (primary) black hole slows the alignment process down. We revisit the problem and develop a semi-analytical model to describe the coupling between gas-driven inspiral and spin alignment, finding that binaries with mass ratio q<~0.2 approach the gravitational-wave driven inspiral in differential misalignment: light secondaries prevent primaries from aligning. Binary black holes with misaligned primaries are ideal candidates for precession effects in the strong-gravity regime and may suffer from moderately large (~1500 km/s) recoil velocities.