We perform a detailed shock diagnosis of the Herbig-Haro object HH7, a well-defined bow shock from a protostellar outflow. We first present molecular hydrogen images in the 2-1 S(1) and 1-0 S(1) K -band emission lines. We then introduce revised models for magneto-hydrodynamic bow shocks that incorporate a limited C and O chemistry and account for the shock thickness. We employ these models to interpret the new images as well as ISO data, the line profile, H2position-velocity diagram, optical images and the proper motion. This yields a C-shock model that satisfies the constraints, confirming that ambipolar diffusion is the linchpin in the shock physics. The best model is a slow-moving paraboloidal bow of speed 55 km/s, with a pre-shock density of 8x103/cm3 and an H2/H number ratio of just 0.25. The bow moves at an angle of ∼30° to the line of sight and at a position angle of ∼95° in the plane of the sky rather than along the outflow axis of ∼123°. The bow model also predicts the observed low line emission from H2O, without the need for gas-phase depletion. Predictions for imaging and spectroscopy at far-infrared wavelengths, employing the 63-µm [Oi] line, are presented.