Approaches to improving multilingual language understanding often require multiple languages during the training phase, rely on complicated training techniques, and -- importantly -- struggle with significant performance gaps between high-resource and low-resource languages. We hypothesize that the performance gaps between languages are affected by linguistic gaps between those languages and provide a novel solution for robust multilingual language modeling by employing phonemic representations (specifically, using phonemes as input tokens to LMs rather than subwords). We present quantitative evidence from three cross-lingual tasks that demonstrate the effectiveness of phonemic representation, which is further justified by a theoretical analysis of the cross-lingual performance gap.