Leveraging supervised information can lead to superior retrieval performance in the image hashing domain but the performance degrades significantly without enough labeled data. One effective solution to boost performance is to employ generative models, such as Generative Adversarial Networks (GANs), to generate synthetic data in an image hashing model. However, GAN-based methods are difficult to train, which prevents the hashing approaches from jointly training the generative models and the hash functions. This limitation results in sub-optimal retrieval performance. To overcome this limitation, we propose a novel framework, the generative cooperative hashing network, which is based on energy-based cooperative learning. This framework jointly learns a powerful generative representation of the data and a robust hash function via two components: a top-down contrastive pair generator that synthesizes contrastive images and a bottom-up multipurpose descriptor that simultaneously represents the images from multiple perspectives, including probability density, hash code, latent code, and category. The two components are jointly learned via a novel likelihood-based cooperative learning scheme. We conduct experiments on several real-world datasets and show that the proposed method outperforms the competing hashing supervised methods, achieving up to 10\% relative improvement over the current state-of-the-art supervised hashing methods, and exhibits a significantly better performance in out-of-distribution retrieval.