Cooperative perception in autonomous driving promises to overcome single-agent limitations like sensor occlusion, but its real-world application is critically hindered by inter-agent pose errors. While existing methods attempt to correct these errors by aligning landmarks derived from 3D object detections, they suffer from outlier landmarks as imperfect perception can bias the calibration process. In this paper, we propose MH-V2X, a novel framework that recasts robust cooperative perception as a probabilistic inference problem. Inspired by robust estimation techniques, we generate an ensemble of diverse pose hypotheses by performing calibration on random subsets of landmarks, ensuring a high likelihood of capturing a highly accurate pose. We design probabilistic detections to quantify its own uncertainty for each prediction. Finally, we introduce a principled Bayesian fusion mechanism that treats each prediction as a noisy observation, obtaining a robust perception output under a posterior inference paradigm. Extensive experiments on large-scale V2X datasets demonstrate that our approach enhances perception performance under a wide range of pose error conditions.