In a rotating two-phase sample of ³He-B and magnetic-field stabilized ³He-A the large difference in mutual friction dissipation at 0.20Tc gives rise to unusual vortex flow responses.We use noninvasive NMR techniques to monitor spin down and spin up of the B-phase superfluid component to a sudden change in the rotation velocity. Compared to measurements at low field with no A phase, where these responses are laminar in cylindrically symmetric flow, spin down with vortices extending across the AB interface is found to be faster, indicating enhanced dissipation from turbulence. Spin up in turn is slower, owing to rapid annihilation of remanent vortices before the rotation increase. As confirmed by both our NMR signal analysis and vortex filament calculations, these observations are explained by the additional force acting on the B phase vortex ends at the AB interface.