Constructing a high-fidelity cross-scale numerical model is the primary challenge in the multiscale analysis of multiphase medium composites. Considering the limitations of the Finite Element Method (FEM) in the study of the dynamic damage problem of non-homogeneous and discontinuous materials, the Discrete Element Method (DEM) is used in this study to build a three-medium multiscale numerical model containing aggregates, matrix, and microcapsules. Further, the dynamic damage problem of microcapsules embedded in self-healing composites and the damage competition issues between the microcapsules and the matrix are investigated. The results indicate that (1) The damage evolution process, the location of maximum damage, and the final damage pattern of microcapsule embedded in the matrix and exposed to the ideal environment differed considerably. (2) The effect of microcapsule volume fraction on the mechanical strength of the matrix in self-healing composites is not linearly negatively correlated, but instead, there is a non-linear relationship, which is highly dependent on the strength ratio of the microcapsule to the matrix. (3) In self-healing composites, damage competition between the microcapsules and the matrix has a decisive influence on triggering the self-healing mechanism. (4) To obtain a better self-healing effect, the microcapsule volume fraction in the self-healing composites should not exceed 1.5%, and the mechanical strength pre-maintenance should not be more than 95% of the failure strength. The multiphase medium & multiscale analysis method proposed in this study also provides a new approach for visualizing the progressive dynamic damage problem in self-healing composites.