This work presents a design-space dimensionality reduction method, namely parametric model embedding (PME), for structural optimization [1]. The PME is applied for the multidisciplinary and topology optimization of a generic prismatic planing hull (GPPH). PME leverages principal component analysis (PCA) to identify dominant directions in a space of geometry-based features, integrating the original design parameters into the PCA formulation through weighting matrices. This formulation allows both physical interpretability of the reduced design space and the possibility to use the original parameterization during the optimization process. The multidisciplinary optimization is performed using two nested loops. In the outer loop the hydrodynamic optimization is carried out by multi-fidelity optimization of the length, beam, and draft. This loop addresses the resistance and slamming loads reduction and displacement increase, considering realistic hydrodynamic loads of the GPPH advancing in waves and evaluated by computational fluid dynamics. In the inner loop the structural optimization is performed. This loop addresses the weight reduction while preserving the structural safety, evaluated by computational structural dynamics. A significant challenge is the high-dimensional nature of the structural design space, which involves a variable number of elements, each one with its characteristics, leading to a mixed-integer problem with up to 800 variables. By applying PME, the dimensionality is reduced by 99% while still representing 95% of the original variability, mapping the mixed-integer topology and structural choices into a continuous latent manifold and rendering the process computationally tractable. Results demonstrate that the proposed method identifies hull configurations achieving a 20% weight reduction and a 35% improvement in hydrodynamic resistance, while satisfying structural safety constraints. Acknowledgments: Funding for this work is provided by the Office of Naval Research, Ship Systems and Engineering Research Division (Code 331), Small Craft S&T Program, Program Officer Dr. Robert Brizzolara, Grants N00014-22-1-2413 and N00014-25-1-2283. Erik Kubina and his team from NSWCCD are funded under Grant O2411017017043184 under administration of Dr. Robert Brizzolara. The work is conducted in collaboration with NATO STO AVT task group on ''Enhanced Design Processes of Military Vehicles through Machine Learning Methods'' (AVT-404).