Multiple image hiding aims to hide multiple secret images into a single cover image, and then recover all secret images perfectly. Such high-capacity hiding may easily lead to contour shadows or color distortion, which makes multiple image hiding a very challenging task. In this paper, we propose a novel multiple image hiding framework based on invertible neural network, namely DeepMIH. Specifically, we develop an invertible hiding neural network (IHNN) to innovatively model the image concealing and revealing as its forward and backward processes, making them fully coupled and reversible. The IHNN is highly flexible, which can be cascaded as many times as required to achieve the hiding of multiple images. To enhance the invisibility, we design an importance map (IM) module to guide the current image hiding based on the previous image hiding results. In addition, we find that the image hidden in the high-frequency sub-bands tends to achieve better hiding performance, and thus propose a low-frequency wavelet loss to constrain that no secret information is hidden in the low-frequency sub-bands. Experimental results show that our DeepMIH significantly outperforms other state-of-the-art methods, in terms of hiding invisibility, security and recovery accuracy on a variety of datasets.