Ultrasound-induced bubble oscillation in liquids is a key physical mechanism underlying numerous biomedical and environmental technologies. Under high-intensity acoustic excitation, bubbles may undergo rapid expansion and collapse accompanied by highly nonlinear phenomena, including asymmetric deformation, shock generation, and high-speed microjet formation. These events can impose substantial mechanical loading on nearby compliant solids, such as soft biological tissues. Despite its importance, reliable numerical prediction of ultrasound-driven bubble behavior interacting with deformable solids remains difficult because of strong compressibility, extreme interface distortion, and the challenge of preserving mass in multiphase simulations. In this study, we present a mass-conservative computational framework for modeling compressible multiphase flows coupled with viscoelastic solid deformation under ultrasonic excitation. The method employs a coupled level-set and volume-of-fluid (CLSVOF) strategy, in which interface geometry is reconstructed from the volume-conservative VOF field using interface normals obtained from the smooth level-set function. Deformation of the solid is described using a fully Eulerian formulation based on the left Cauchy–Green deformation tensor, enabling the simulation of viscoelastic neo-Hookean materials without mesh distortion or remeshing. The proposed framework is validated through a series of benchmark tests involving multiphase flow, interface stability, and solid deformation, showing strong agreement with established reference results. Simulations of acoustically driven bubble dynamics closely match predictions from the Keller–Miksis model while maintaining excellent mass conservation. Parametric studies further explore bubble–tissue interactions, revealing the influence of material stiffness and initial separation distance on deformation intensity. Overall, the developed CLSVOF framework offers a robust and flexible tool for investigating complex ultrasound-driven fluid–solid interaction phenomena.