Owing to the different imaging mechanisms between sensors, significant nonlinear radiometric differences exist among multimodal remote-sensing images, thus rendering image registration challenging. Hence, a dual-stage multimodal image-registration method based on structural information is proposed. In the coarse registration stage, the RIFT algorithm is combined with log-Gabor filters to extract the structural information of the images and construct a maximum index map. FREAK descriptors are constructed to describe key features, thus eliminating differences in feature descriptions under different sensor imaging conditions. In the fine registration stage, a dense three-dimensional template-structure feature representation is designed based on log-Gabor convolution image information, and a three-dimensional phase-correlation matching strategy is adopted for feature correspondence, thereby further improving the registration accuracy and efficiency. Experimental validation on six multimodal remote sensing datasets, including optical-optical, optical-infrared, optical-depth, optical-map, optical-SAR, and day-night, shows that this method outperforms the SAR-SIFT, RIFT, and SRIF algorithms across all metrics. The number of correct matches are 123.91 times, 4.09 times, and 2.82 times higher than the above algorithms, respectively, thus demonstrating the significant advantages and robustness of the proposed algorithm.