By supporting multi-modal retrieval training and evaluation, image captioning datasets have spurred remarkable progress on representation learning. Unfortunately, datasets have limited cross-modal associations: images are not paired with other images, captions are only paired with other captions of the same image, there are no negative associations and there are missing positive cross-modal associations. This undermines research into how inter-modality learning impacts intra-modality tasks. We address this gap with Crisscrossed Captions (CxC), an extension of the MS-COCO dataset with human semantic similarity judgments for 267,095 intra- and inter-modality pairs. We report baseline results on CxC for strong existing unimodal and multimodal models. We also evaluate a multitask dual encoder trained on both image-caption and caption-caption pairs that crucially demonstrates CxC's value for measuring the influence of intra- and inter-modality learning.