A high fidelity assessment of accumulative damage of woven fabric composite structures subjected to aggressive loadings is strongly reliant on the accurate characterization of the inherent multi-scale microstructures and the underlying deformation phenomena. Damage in composite sandwich and joint structures is characterized by the coexistence of discrete (delamination) and continuum damage (matrix cracking and intralaminar damage). A purely fracture mechanics-based or a purely continuum damage mechanics-based tool alone cannot effectively characterize the interaction between the discrete and continuum damage and their compounding effect that leads to the final rupture. In this paper, a hybrid discrete and continuum damage model is developed and numerically implemented within the LS-DYNA environment via a user-defined material model. The continuum damage progression and its associated stiffness degradation are predicted based on the constituent stress/strain and their associated failure criteria while the discrete delamination damage is captured via a cohesive interface model. A multi-scale computational framework is established to bridge the response and failure predictions at constituent, ply, and laminated composite level. The calculated constituent stress and strain are used in a mechanism-driven failure criterion to predict the failure mode, failure sequence, and the synergistic interaction that leads to global stiffness degradation and the final rupture, The use of the cohesive interface model can capture the complicated delamination zone without posing the self-similar crack growth condition. The unified depiction of the continuum and discrete damage via the damage mechanics theory provides a rational way to study the coupling effects between the in-plane and the out-of-plane failure modes. The applicability and accuracy of the damage models used in the hybrid dynamic failure prediction tool are demonstrated via its application to a circular plate and a composite hat stiffener subjected to shock and low velocity impact loading. The synergistic interaction between the continuum and discrete damage is explored via its application to a sandwich beam subjected to a low velocity impact.