This paper introduces BD2BB, a novel language and vision benchmark that requires multimodal models combine complementary information from the two modalities. Recently, impressive progress has been made to develop universal multimodal encoders suitable for virtually any language and vision tasks. However, current approaches often require them to combine redundant information provided by language and vision. Inspired by real-life communicative contexts, we propose a novel task where either modality is necessary but not sufficient to make a correct prediction. To do so, we first build a dataset of images and corresponding sentences provided by human participants. Second, we evaluate state-of-the-art models and compare their performance against human speakers. We show that, while the task is relatively easy for humans, best-performing models struggle to achieve similar results.