A nonlinear inertial-aided image-based visual servo control approach for the stabilization of (almost) fully actuated autonomous underwater vehicles (AUVs) is proposed. It makes use of the homography matrix between two images of a planar scene as feedback information while the system dynamics are exploited in a cascade manner in a control design: An outer-loop control defines a reference setpoint based on the homography matrix and an inner-loop control ensures the stabilization of the setpoint by assigning the thrust and torque controls. Unlike conventional solutions that only consider the system kinematics, the proposed control scheme is novel in considering the full system dynamics (incorporating all degrees of freedom, nonlinearities, and couplings, as well as interactions with the surrounding fluid) and in not requiring information of the relative depth and normal vector of the observed scene. Augmented with integral corrections, the proposed controller is robust with respect to model uncertainties and disturbances. The almost global asymptotic stability of the closed-loop system is demonstrated, which is the largest domain of attraction one can achieve by means of continuous feedback control. Simulation results illustrating these properties on a realistic AUV model subjected to a sea current are presented and finally experimental results on a real AUV are reported.