In disaster emergency response, providing timely situational awareness information presents a significant challenge, particularly when ground infrastructure is compromised. To address this issue, this study introduces a multilayered, heterogeneous unmanned aerial vehicle (UAV)-assisted network designed for efficient information delivery. Low latency is achieved through the integrated optimization of proactive caching and three-dimensional (3D) UAV deployment. The joint optimization problem is formulated as a complex mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve. Therefore, we decompose the primary issue into two sub-problems: One focusing on the caching strategy and the other on the UAV deployment strategy. The caching sub-problem is an non-deterministic polynomial-time hard (NP-hard) knapsack problem. To effectively balance the transmission speed and completeness of emergency information, this work develops two novel caching algorithms: Hot information priority (HIP) and diversified information priority (DIP). Regarding UAV deployment, the 3D placement problem is inherently non-convex. We further divide it into horizontal position optimization and vertical height optimization. The horizontal position optimization can be reformulated as a convex optimization problem. The vertical height optimization problem is theoretically proven to be quasiconvex and can be efficiently solved. Simulation results demonstrate that the proposed framework markedly reduces the latency of information dissemination in UAV-assisted emergency networks.