Robotic catching has traditionally focused on single-handed systems, which are limited in their ability to handle larger or more complex objects. In contrast, bimanual catching offers significant potential for improved dexterity and object handling but introduces new challenges in coordination and control. In this paper, we propose a novel framework for learning dexterous bimanual catching skills using Heterogeneous-Agent Reinforcement Learning (HARL). Our approach introduces an adversarial reward scheme, where a throw agent increases the difficulty of throws-adjusting speed-while a catch agent learns to coordinate both hands to catch objects under these evolving conditions. We evaluate the framework in simulated environments using 15 different objects, demonstrating robustness and versatility in handling diverse objects. Our method achieved approximately a 2x increase in catching reward compared to single-agent baselines across 15 diverse objects.