Inspecting indoor environments such as tunnels, industrial facilities, and construction sites is essential for infrastructure monitoring and maintenance. While manual inspection in these environments is often time-consuming and potentially hazardous, Unmanned Aerial Vehicles (UAVs) can improve efficiency by autonomously handling inspection tasks. Such inspection tasks usually rely on reference maps for coverage planning. However, in industrial applications, only the floor plans are typically available. The unforeseen obstacles not included in the floor plans will result in outdated reference maps and inefficient or unsafe inspection trajectories. In this work, we propose an adaptive inspection framework that integrates global coverage planning with local reactive adaptation to improve the coverage and efficiency of UAV-based inspection in partially unknown indoor environments. Experimental results in structured indoor scenarios demonstrate the effectiveness of the proposed approach in inspection efficiency and achieving high coverage rates with adaptive obstacle handling, highlighting its potential for enhancing the efficiency of indoor facility inspection.