The design of autonomous underwater vehicles (AUVs) and their docking stations has been a popular research topic for several decades. Although many AUV and dock designs have been proposed, materialized, and commercialized, most of these existing designs prioritize the functionality of the AUV over the dock, or vise versa; there has been limited formal research in analytical optimization for AUV docking systems. In this paper, a multidisciplinary optimization framework is presented with the aim to fill this theoretical gap. We propose a co-design optimization method that optimizes multiple design parameters governing the archetype of an AUV and its docking system. Capturing the user design intents in the optimization process, the proposed method produces a set of optimal design parameters that satisfies a set of predefined bounds, constraints, and initial conditions. Three cases of design optimization are reported for different design intents. Each optimal design found in the three cases is compared to an existing system to show the validity of this design optimization framework.