This paper introduces a novel evaluation framework, inspired by methods from human psychophysics, to systematically assess the robustness of multimodal integration in audiovisual speech recognition (AVSR) models relative to human abilities. We present preliminary results on AV-HuBERT [Shi et al., 2022a,b] suggesting that multimodal integration in state-of-the-art (SOTA) AVSR models remains mediocre when compared to human performance and we discuss avenues for improvement.