We investigate the nature of stationary structures streaming at subfast magnetosonic speeds perpendicular to the magnetic field in a bi-ion plasma consisting of protons and a heavy ion species in which the magnetic field is frozen into the electrons, whose inertia may be neglected. The study is based on the properties of the structure equation for the system, which is derived from the equations of motion and the Maxwell equations, and therefore reflects the coupling between the two ion fluids and the electrons through the Lorentz forces and charge neutrality. The basic features of the structure equation are elucidated by making use of conservation of total momentum and charge neutrality, which provide relations between the ion speeds in the unperturbed flow direction and the electron speed. This combination of relations, which we call the momentum hodograph of the system, reveals the structure of the flow and the magnetic field in a solitary-type pulse. In particular, we find that in the initial portion of a compressive soliton, heavy ions run ahead of the electrons and the protons lag between them until a point is reached where they all once more attain the same speed, after which the protons run ahead and are accelerated whereas the heavies now lag behind the continuously decelerating electrons. The second half of the wave is a mirror image of the first portion. The strength of the compression (the amplitude of the wave) is determined from the momentum hodograph, and depends upon the initial Mach number, abundance ratio of heavies to protons and the mass ratio. The analysis is relevant to subfast flows of mass-loaded plasmas and pile-up boundaries, which appear near comets and non-magnetic planets.