Several solutions for stationary models for the plasma flow configuration in the interface region between the unperturbed flows of the interstellar plasma and the supersonic solar wind plasma have been discussed in the literature. The magnetohydrodynamic form of an interaction of these counterstreaming flows establishes a free pressure equilibrium surface, called the heliopause, with a frontal nose part in the upwind direction and a cylindrical tail extending into the downflow direction. There is, however, a need to discuss whether or not the proposed heliopause configurations can be expected to be stable with respect to magnetohydrodynamical or hydrodynamical perturbations caused by time-dependent or turbulent structures in the counterflowing plasmas. In a foregoing paper we have studied the stability of the heliopause boundary surface with respect to purely hydrodynamical perturbations. In this paper here, we in addition take into account interstellar magnetic fields at the heliopause and investigate their influence on the stability of this layer. Again it turns out that this problem is of a different quality in the nose region and in the off-nose region (the flanks) of the heliopause. However, it is shown here that compared to the purely hydrodynamic case magnetic fields can have a strongly stabilizing effect at those heliopause regions where the outer LISM fields are parallel to the shear velocities of the adjacent plasmas. We especially devote attention to these latter regions and investigate the general forms of MHD Kelvin-Helmholtz instabilities for the prevailing transition conditions in compressible plasmas. We show that the part in the off-nose region of the heliopause, where the Mach number of the shocked solar wind flow is smaller than some critical value defined by the undisturbed flow parameters, is stable with respect to short wavelength disturbances. In any case, however, this critical Mach number is smaller than unity. On the other hand, this means that the part of the off-nose heliopause region where the shocked solar wind flow becomes supersonic cannot be stabilized by the interstellar magnetic field, no matter how strong it is.
