Vision-language pretraining (VLP) with transformers has demonstrated exceptional performance across numerous multimodal tasks. However, the adversarial robustness of these models has not been thoroughly investigated. Existing multimodal attack methods have largely overlooked cross-modal interactions between visual and textual modalities, particularly in the context of cross-attention mechanisms. In this paper, we study the adversarial vulnerability of recent VLP transformers and design a novel Joint Multimodal Transformer Feature Attack (JMTFA) that concurrently introduces adversarial perturbations in both visual and textual modalities under white-box settings. JMTFA strategically targets attention relevance scores to disrupt important features within each modality, generating adversarial samples by fusing perturbations and leading to erroneous model predictions. Experimental results indicate that the proposed approach achieves high attack success rates on vision-language understanding and reasoning downstream tasks compared to existing baselines. Notably, our findings reveal that the textual modality significantly influences the complex fusion processes within VLP transformers. Moreover, we observe no apparent relationship between model size and adversarial robustness under our proposed attacks. These insights emphasize a new dimension of adversarial robustness and underscore potential risks in the reliable deployment of multimodal AI systems.