The Kelvin-Helmholtz instability is well known in classical hydrodynamics where it explains the sudden emergence of interfacial surface waves as a function of the flow velocity parallel to the interface. It can be carried over to the inviscid two-fluid dynamics of superfluids, to describe the stability of the phase boundary separating two bulk phases of superfluid He3 in rotating flow when the boundary is localized with a magnetic-field gradient. The results from extensive measurements as a function of temperature and pressure confirm that in the superfluid the classic condition for stability is changed and that the magnetic polarization of the B phase at the phase boundary has to be taken into account, which yields the magnetic-field-dependent interfacial surface tension.