The role of slow-mode magnetohydrodynamic (MHD) shocks in magnetic reconnection is of great importance for energy conversion and transport, but in many astrophysical plasmas the plasma is not fully ionised. In this paper, we use numerical simulations to investigate the role of collisional coupling between a proton-electron, charge-neutral fluid and a neutral hydrogen fluid for the one-dimensional (1D) Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field. This system, in the MHD limit, is characterised by two waves. The first is a fast-mode rarefaction wave that drives a flow towards a slow-mode MHD shock wave. The system evolves through four stages: initiation, weak coupling, intermediate coupling, and a quasi-steady state. The initial stages are characterised by an over-pressured neutral region that expands with characteristics of a blast wave. In the later stages, the system tends towards a self-similar solution where the main drift velocity is concentrated in the thin region of the shock front. Because of the nature of the system, the neutral fluid is overpressured by the shock when compared to a purely hydrodynamic shock, which results in the neutral fluid expanding to form the shock precursor. Once it has formed, the thickness of the shock front is proportional to ξi-1.2, which is a smaller exponent than would be naively expected from simple scaling arguments. One interesting result is that the shock front is a continuous transition of the physical variables of subsonic velocity upstream of the shock front (a c-shock) to a sharp jump in the physical variables followed by a relaxation to the downstream values for supersonic upstream velocity (a j-shock). The frictional heating that results from the velocity drift across the shock front can amount to ∼2 per cent of the reference magnetic energy.