A charged projectile generates an electrostatic wake as it moves through a background plasma. This wake normally gives rise to a drag force that acts antiparallel to the velocity vector of the projectile, and is commonly referred to as the stopping power. A recent theory (Lafleur T and Baalrud S D 2019 Plasma Phys. Control. Fusion61 125 004) predicted that an additional component of the friction force that is perpendicular to both the projectile velocity and the Lorentz force arises when a plasma is strongly magnetized. We extend the previous analysis of this transverse friction force, which was based on the one-component plasma model, to treat a two-component charge-neutral electron-ion plasma. The direction and magnitude of the transverse force is found to depend on the projectile speed relative to the electron and ion thermal velocities, and to change sign three times. For projectile speeds below a certain threshold, the transverse force is dominated by collisions with ions, while above this threshold, only electron collisions contribute. The average trajectory of the projectile is significantly altered by the transverse force as it slows.