This paper addresses the robustness problem of visual-inertial state estimation for underwater operations. Underwater robots operating in a challenging environment are required to know their pose at all times. All vision-based localization schemes are prone to failure due to poor visibility conditions, color loss, and lack of features. The proposed approach utilizes a model of the robot's kinematics together with proprioceptive sensors to maintain the pose estimate during visual-inertial odometry (VIO) failures. Furthermore, the trajectories from successful VIO and the ones from the model-driven odometry are integrated in a coherent set that maintains a consistent pose at all times. Health-monitoring tracks the VIO process ensuring timely switches between the two estimators. Finally, loop closure is implemented on the overall trajectory. The resulting framework is a robust estimator switching between model-based and visual-inertial odometry (SM/VIO). Experimental results from numerous deployments of the Aqua2 vehicle demonstrate the robustness of our approach over coral reefs and a shipwreck.