This paper demonstrates robust damping of interarea oscillations in an AC-Multiterminal DC (MTDC) grid following major contingencies like the outage of a converter pole and line outage. Damping controller design based on H∞ mixed-sensitivity formulation in the Linear Matrix Inequality (LMI) framework has been performed. Emphasis has been placed on achieving robustness in the design by incorporating proper weighing filters for disturbance rejection and control energy minimization. The proposed controller uses feedback signals from remote locations and modulates the real power reference of two converter poles in a converter station of the asymmetric bipolar MTDC grid, which is integrated with AC systems. A 6-machine 3-area system and a 16-machine, 5-area system were used as the AC test systems. Robustness in damping performance in case of converter outage and AC line outage was successfully achieved by the designed controllers in both the test systems.