Recent advancements in machine learning have spotlighted the potential of hyperbolic spaces as they effectively learn hierarchical feature representations. While there has been progress in leveraging hyperbolic spaces in single-modality contexts, its exploration in multimodal settings remains under explored. Some recent efforts have sought to transpose Euclidean multimodal learning techniques to hyperbolic spaces, by adopting geodesic distance based contrastive losses. However, we show both theoretically and empirically that such spatial proximity based contrastive loss significantly disrupts hierarchies in the latent space. To remedy this, we advocate that the cross-modal representations should accept the inherent modality gap between text and images, and introduce a novel approach to measure cross-modal similarity that does not enforce spatial proximity. Our approach show remarkable capabilities in preserving unimodal hierarchies while aligning the two modalities. Our experiments on a series of downstream tasks demonstrate that better latent structure emerges with our objective function while being superior in text-to-image and image-to-text retrieval tasks.