A dual-shearing interferometer (DSI) for multimodal hyperspectral imaging is presented. Two orthogonally stacked pairs of coherent beams are generated by a pair of novel, to the best of our knowledge, birefringent lateral shearing splitters. Consequently, two sets of interferograms with full pixel resolution are captured alternately in a time sequence in the double Nyquist frequency mode. Modals of dual-field-of-view hyperspectral imaging and differential-polarization hyperspectral imaging are introduced, and verification experiments are performed. The feasibility of other modals is discussed. The proposed method can effectively improve the instrument's performance in terms of the field of view, polarization, spectral resolution, and spectral range.