This study develops a computational framework for the vibroacoustic analysis of a CFRP laminated plate embedded with a circular Acoustic Black Hole (ABH) and coupled to a rectangular acoustic cavity. Building on recent vibroacoustic modelling of laminated plates and ABH–cavity systems, an extended Gaussian Expansion Method (GEM) is employed to represent both plate deformation and cavity pressure within a unified Rayleigh-Ritz formulation. The Gaussian basis enables accurate modelling of the strong spatial gradients induced by the ABH profile while accommodating laminate anisotropy, elastic restraints, and damping layers. Interface coupling is enforced through normal velocity continuity, allowing for the prediction of both modal and forced responses. The semi-analytical results show excellent agreement with finite element simulations from COMSOL Multiphysics®. Parametric studies demonstrate how ABH geometry, residual thickness, and damping influence sound radiation into the cavity, confirming the effectiveness of ABH features in reducing noise in composite structures.