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This paper addresses the problem of online inverse reinforcement learning for nonlinear systems with modeling uncertainties while in the presence of unknown disturbances. The developed approach observes state and input trajectories for an agent and identifies the unknown reward function online. Sub-optimality introduced in the observed trajectories by the unknown external disturbance is compensated for using a novel model-based inverse reinforcement learning approach. The observer estimates the external disturbances and uses the resulting estimates to learn the dynamic model of the demonstrator. The learned demonstrator model along with the observed suboptimal trajectories are used to implement inverse reinforcement learning. Theoretical guarantees are provided using Lyapunov theory and a simulation example is shown to demonstrate the effectiveness of the proposed technique.