Multispectral and multimodal image processing is important in the community of computer vision and computational photography. As the acquired multispectral and multimodal data are generally misaligned due to the alternation or movement of the image device, the image registration procedure is necessary. The registration of multispectral or multimodal image is challenging due to the non-linear intensity and gradient variation. To cope with this challenge, we propose the phase congruency network (PCNet), which is able to enhance the structure similarity and alleviate the non-linear intensity and gradient variation. The images can then be aligned using the similarity enhanced features produced by the network. PCNet is constructed under the guidance of the phase congruency prior. The network contains three trainable layers accompany with the modified learnable Gabor kernels according to the phase congruency theory. Thanks to the prior knowledge, PCNet is extremely light-weight and can be trained on quite a small amount of multispectral data. PCNet can be viewed to be fully convolutional and hence can take input of arbitrary sizes. Once trained, PCNet is applicable on a variety of multispectral and multimodal data such as RGB/NIR and flash/no-flash images without additional further tuning. Experimental results validate that PCNet outperforms current state-of-the-art registration algorithms, including the deep-learning based ones that have the number of parameters hundreds times compared to PCNet. Thanks to the similarity enhancement training, PCNet outperforms the original phase congruency algorithm with two-thirds less feature channels.