Palmprint recognition has recently attracted broad attention due to its rich discriminative features, contactless collection manner and less invasive. However, most existing methods focus on within-illumination palmprint recognition, which requires the similar illumination of query samples acquisition as the gallery samples, significantly limiting its practical applications in the open environment. In this paper, we propose a cross-illumination palmprint recognition method by jointly learning the unified binary feature descriptors of multiple illumination palmprint images. Given two different illuminations of palmprint images, we first calculate the direction-based ordinal measure vectors (DOMVs) to sample the important palmprint direction features. Then, we jointly learn a unified feature mapping that project the two-illumination DOMVs into binary feature codes. To better exploit the palm-invariant features of multi-illumination samples, we make the binary feature codes as similar as possible by minimizing the feature distance between the two illumination samples of the same palm. Moreover, we maximize the variances of all binary feature codes among the training samples for each illumination, such that the discriminative power can be enhanced in an unsupervised manner. Finally, we convert the binary feature codes of a palmprint image into a block-wise histogram feature descriptor for cross-illumination palmprint recognition. Experimental results on three cross-illumination palmprint datasets show that our proposed method achieves competitive cross-illumination palmprint recognition performance in comparison with the state-of-the-art palmprint feature descriptors.