The goal of infrared and visible image fusion is to generate an informative image that preserves the complementary information of the two types of source images, such as texture details and infrared targets. Existing methods have designed a variety of means to achieve the fusion of image texture and target complementary information. But they ignore the fact that the two types of source images have the complementarity of illumination, especially the infrared image can mainly supplement the information of the low-light visible image. An image fusion method using infrared and visible light to supplement light interactively is proposed. It performs intrinsic image decomposition on the input infrared and visible light images respectively and then fuses the illumination components and material components of the two types of images respectively. Further, to better meet the needs of image fusion, an improved variational model for the decomposition of image intrinsics is proposed. Experimental results demonstrate the effectiveness of the proposed model with its algorithm. Compared with the state-of-the-art methods, the significant advantage of the proposed method is that it has better fusion accuracy and visual perception at the same time, and the comprehensive metric evaluation is the best (9.2% performance improvement). The code is available at https://github.com/skyworkds/IFICI.