Multi-Intensity Illuminated Infrared (MIIR) video is a new type of infrared video which solves the problem of improper illumination conditions for ordinary infrared cameras for nighttime surveillance. However, its time-varying intensity makes it hard to be compressed with traditional video coding methods. In this paper we use MV-HEVC and 3D-HEVC video coding standards, which are originally designed for Multi-view and 3D video coding, to compress the MIIR videos. With the proposed encoding method, the coding structures of MV- and 3D-HEVC can be employed to compress the MIIR video in a more efficient way. Experimental results show that the coding structures of MV- and 3D-HEVC can compress such video in a more efficient way, i.e., up to 43.8%/50.1% bitrate reductions with MV/3D-HEVC compared with standalone HEVC compression and 74.3%/80.5% bitrate reductions compared with simulcast HEVC coding in the enhancement layers.