Recently, many Near infrared-visible (NIR-VIS) heterogeneous face recognition (HFR) methods have been proposed in the community. But it remains a challenging problem because of the sensing gap along with large pose variations. In this paper, we propose an Exemplar Guided Cross-Spectral Face Hallucination (EGCH) to reduce the domain discrepancy through disentangled representation learning. For each modality, EGCH contains a spectral encoder as well as a structure encoder to disentangle spectral and structure representation, respectively. It also contains a traditional generator that reconstructs the input from the above two representations, and a structure generator that predicts the facial parsing map from the structure representation. Besides, mutual information minimization and maximization are conducted to boost disentanglement and make representations adequately expressed. Then the translation is built on structure representations between two modalities. Provided with the transformed NIR structure representation and original VIS spectral representation, EGCH is capable to produce high-fidelity VIS images that preserve the topology structure of the input NIR while transfer the spectral information of an arbitrary VIS exemplar. Extensive experiments demonstrate that the proposed method achieves more promising results both qualitatively and quantitatively than the state-of-the-art NIR-VIS methods.