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 light image. Extensive work has been conducted on studying the statistics of natural LWIR and visible images. Nonetheless, there has been little work done on analyzing the statistics of fused LWIR and visible images and associated distortions. In this paper, we analyze five multi-resolution-based image fusion methods in regards to several common distortions, including blur, white noise, JPEG compression, and non-uniformity. We study the natural scene statistics of fused images and how they are affected by these kinds of distortions. Furthermore, we conducted a human study on the subjective quality of pristine and degraded fused LWIR-visible images. We used this new database to create an automatic opinion-distortion-unaware fused image quality model and analyzer algorithm. In the human study, 27 subjects evaluated 750 images over five sessions each. We also propose an opinion-aware fused image quality analyzer, whose relative predictions with respect to other state-of-the-art models correlate better with human perceptual evaluations than competing methods. An implementation of the proposed fused image quality measures can be found at https://github.com/ujemd/NSS-of-LWIR-and-Vissible-Images. Also, the new database can be found at http://bit.ly/2noZlbQ.