The ability to efficiently plan and execute search missions in challenging and complex environments during natural and man-made disasters is imperative. In many emergency situations, precise navigation between obstacles and time-efficient searching around 3D structures is essential for finding survivors. In this work we propose an integrated assessment and search planning approach which allows an autonomous UAV (unmanned aerial vehicle) agent to plan and execute collision-free search trajectories in 3D environments. More specifically, the proposed search-planning framework aims to integrate and automate the first two phases (i.e., the assessment phase and the search phase) of a traditional search-and-rescue (SAR) mission. In the first stage, termed assessment-planning we aim to find a high-level assessment plan which the UAV agent can execute in order to visit a set of points of interest. The generated plan of this stage guides the UAV to fly over the objects of interest thus providing a first assessment of the situation at hand. In the second stage, termed search-planning, the UAV trajectory is further fine-tuned to allow the UAV to search in 3D (i.e., across all faces) the objects of interest for survivors. The performance of the proposed approach is demonstrated through extensive simulation analysis.