The capability to automatically evaluate the quality of long wave infrared (LWIR) and visible light images has the potential to play an important role in determining and controlling the quality of a resulting fused LWIR-visible image. Extensive work has been conducted on studying the statistics of natural LWIR and visible light images. Nonetheless, there has been little work done on analyzing the statistics of fused images and associated distortions. In this paper, we study the natural scene statistics (NSS) of fused images and how they are affected by several common types of distortions, including blur, white noise, JPEG compression, and non-uniformity (NU). Based on the results of a separate subjective study on the quality of pristine and degraded fused images, we propose an opinion-aware (OA) fused image quality analyzer, whose relative predictions with respect to other state-of-the-art metrics correlate better with human perceptual evaluations.