The dissipative, mass-loading, multifluid model, developed by Zank et al. [1993, 1994> to describe the structurally complex bow shocks observed at comets, has been extended to include the effects of a magnetic field. After describing the model, the shock structure problem associated with the one-dimensional, steady state conservation equations is solved. The solutions are compared to those obtained from previous cold and warm gasdynamic models. The characteristic speeds of the system are calculated, and it is found that the physically relevant solutions correspond to fast magnetosonic shocks. The extended multifluid model is used to explore a new type of wave, called an ''MHD draping shock,'' which was proposed by Neubauer et al. [1990> to explain the unusual behavior of the magnetic field across the outbound Halley bow shock. It is found that mass loading induces switch-on behavior at quasi-parallel shocks, even in a high plasma beta environment. Across quasi-parallel shocks we find switch-on rotations as large as 30¿ in the cold solar wind case. This value decreases with increasing solar wind plasma beta, to a value of 16¿ at a value of &bgr;sw=1. We do not find rotations large enough to explain the 69¿ twist in the field observed by Giotto, nor do we find any cases where the perpendicular component of the field changes sign. ¿ American Geophysical Union 1996