Marine power systems are exposed to conservative designs due to strict redundancy and reliability requirements. Moreover, the lack of standard models may hinder the development of green solutions, such as electrification and hybridization. This article proposes a model-based design approach for the stability-compliant development of emerging marine hybrid power systems (HPSs) with increasing application of dc grid, marine batteries, and all-electric propulsion. The proposed approach is established based on three main phases: model development for the power and propulsion system, analytical stability identification, and conceptual design and verification. First, a complete model of the multiphysics dynamical system is developed including the electro-mechanical sub-systems such as engine-generator sets, batteries, power electronics, and associated controllers. The physical and control sub-systems are modeled as building blocks in the state-space formulation. Then, an eigenvalue-based stability framework, namely, stability portrait, is developed to identify the border of system stability with respect to design parameters. Considering system boundaries, the border of stability is drawn with the variation of selected parameters such as filters, dc bus, and engine speed and loading. Selected design scenarios are then evaluated to reach a final conceptual design that ensures system stability while benefiting from the potential efficiency and flexibility of the hybrid system. The analytical models are validated with experimental data.