Underwater explosion (UNDEX) events involve complex physical phenomena and can be categorized into three stages: initial shock wave propagation, cavitation, and bubble pulsation. This study focuses on double UNDEX bubbles, elucidating their highly nonlinear interactions across these stages. Both synchronous and asynchronous explosion cases are examined, with a particular emphasis on assessing the influence of phase change. Employing the 3-D high-fidelity computational framework that incorporates the physics-based cavitation model and non-ideal equations of state for water and explosion gas properties, we conduct validations with field experimental data on single bubbles and extend our analysis to double bubbles. Our principal finding is the interaction between the cavity created by the shock wave and the bubble pulsations. Notably, we discern a significant phase change effect in asynchronous explosion, wherein the vapor cavity region delays the contraction of the previously-generated bubble. This delay is attributed to the low-density region created by the phase change, allowing the bubble to remain expanded for an extended period, thereby enhancing agreement with experimental data. To our knowledge, this study represents the pioneering effort to explore the critical role of phase change in accurately simulating the intricate interactions within double UNDEX scenarios.