We have analyzed the stability of a contact surface located at the ram pressure balance position in a comet coma ionosphere in the presence of collisions between ions and neutrals and finite compressibility. We find that if the surface is taken to be a tangential discontinuity which excludes the interplanetary magnetic field from the ionosphere, this ionopause will be violently unstable to MHD modes. We therefore expect the large-scale magnetic field to permeate the entire coma, even during periods of quiet solar activity. As a result, a stable cometary ionopause may form at a much greater distance from the nucleus.