We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound-state electromagnetic current, as well as the transition currents for the scattering processes [Formula Presented]He[Formula Presented], [Formula Presented], and [Formula Presented]He[Formula Presented]. As a result, a unified covariant three-dimensional description of the [Formula Presented]-[Formula Presented] system is achieved.