Numerous visio-linguistic (V+L) representation learning methods have been developed, yet existing datasets do not adequately evaluate the extent to which they represent visual and linguistic concepts in a unified space. We propose several novel evaluation settings for V+L models, including cross-modal transfer. Furthermore, existing V+L benchmarks often report global accuracy scores on the entire dataset, making it difficult to pinpoint the specific reasoning tasks that models fail and succeed at. We present TraVLR, a synthetic dataset comprising four V+L reasoning tasks. TraVLR’s synthetic nature allows us to constrain its training and testing distributions along task-relevant dimensions, enabling the evaluation of out-of-distribution generalisation. Each example in TraVLR redundantly encodes the scene in two modalities, allowing either to be dropped or added during training or testing without losing relevant information. We compare the performance of four state-of-the-art V+L models, finding that while they perform well on test examples from the same modality, they all fail at cross-modal transfer and have limited success accommodating the addition or deletion of one modality. We release TraVLR as an open challenge for the research community.