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, H2 position-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-1, with a pre-shock density of 8 × 103 cm-3 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.