Object detection plays a crucial role in many security-sensitive applications. However, several recent studies have shown that object detectors can be easily fooled by physically realizable attacks, \eg, adversarial patches and recent adversarial textures, which pose realistic and urgent threats. Adversarial Training (AT) has been recognized as the most effective defense against adversarial attacks. While AT has been extensively studied in the $l_\infty$ attack settings on classification models, AT against physically realizable attacks on object detectors has received limited exploration. Early attempts are only performed to defend against adversarial patches, leaving AT against a wider range of physically realizable attacks under-explored. In this work, we consider defending against various physically realizable attacks with a unified AT method. We propose PBCAT, a novel Patch-Based Composite Adversarial Training strategy. PBCAT optimizes the model by incorporating the combination of small-area gradient-guided adversarial patches and imperceptible global adversarial perturbations covering the entire image. With these designs, PBCAT has the potential to defend against not only adversarial patches but also unseen physically realizable attacks such as adversarial textures. Extensive experiments in multiple settings demonstrated that PBCAT significantly improved robustness against various physically realizable attacks over state-of-the-art defense methods. Notably, it improved the detection accuracy by 29.7\% over previous defense methods under one recent adversarial texture attack.