Adaptive control has been extensively applied to the image-based visual servoing (IBVS) of robots with camera uncertainties. However, parameter convergence in these adaptive systems with linear-in-the-parameters uncertainties relies on a stringent condition termed persistent excitation (PE). Besides, the robot dynamics in the Cartesian space is seldom considered, and the kinematic redundancy of robots is not adequately exploited in existing IBVS methods. This letter proposes a dynamics-based adaptive IBVS method for redundant robots under an eye-to-hand monocular camera with unknown extrinsic and intrinsic parameters, in which a composite learning mechanism is applied to achieve parameter convergence without the PE condition. Compared with existing adaptive IBVS methods, the proposed method requires only a weakened condition termed interval excitation for the exact online estimation of the camera model. Moreover, impedance control is implemented in the nullspace of the visual servo task, such that the robot can avoid damaging interaction but only has tiny influences on the main task. Experiments on a redundant robot with 7 degrees of freedom have validated that the proposed method performs well on parameter estimation, visual regulation, and compliant interaction.