The electron-impact ionization of atomic hydrogen at intermediate excess energies is considered in the situation where the two continuum electrons escape with substantially different velocities and coplanar with the incident direction. Calculations are performed within a model where the three-body final state is described by a product wave function consisting of three symmetrical, Coulomb-type functions. Each of these functions describes the motion of a particular two-body subsystem in the presence of the third charged particle. A comprehensive comparison with available experimental data is presented, and the results are contrasted with those of other theoretical models. Generally, good agreement is found with the absolute measurements; however, in some cases discrepancies between various theoretical predictions and experimental findings are obvious, which highlights the need for a theoretical and experimental benchmark study of these reactions.