Pre-training vision-language models with contrastive objectives has shown promising results that are both scalable to large uncurated datasets and transferable to many downstream applications. Some following works have targeted to improve data efficiency by adding self-supervision terms, but inter-domain (image-text) contrastive loss and intra-domain (image-image) contrastive loss are defined on individual spaces in those works, so many feasible combinations of supervision are overlooked. To overcome this issue, we propose UniCLIP, a Unified framework for Contrastive Language-Image Pre-training. UniCLIP integrates the contrastive loss of both inter-domain pairs and intra-domain pairs into a single universal space. The discrepancies that occur when integrating contrastive loss between different domains are resolved by the three key components of UniCLIP: (1) augmentation-aware feature embedding, (2) MP-NCE loss, and (3) domain dependent similarity measure. UniCLIP outperforms previous vision-language pre-training methods on various single- and multi-modality downstream tasks. In our experiments, we show that each component that comprises UniCLIP contributes well to the final performance.