The heliopause (HP) is the outer edge of the heliosphere which separates the tenuous and hot heliosheath plasma on one side and the relatively dense and cool magnetized interstellar plasma on the other side. As a surface of tangential discontinuity, the HP is subjected to both Rayleigh‐Taylor (RT) and Kelvin‐Helmholtz (KH) instabilities. The coupling between plasma ions and neutral atoms through the process of charge exchange provides an “effective gravity” at the HP, while a shear flow exists across it. We derive analytically the linearized dispersion relation for waves propagating along the surface of this discontinuity, which represents a combined RT/KH analysis. We investigate both the purely hydrodynamic, as well as magnetohydrodynamic, cases, and find that interstellar and heliospheric magnetic fields can help stabilize the HP for RT and KH‐type instabilities.