Large Language Models (LLMs) have demonstrated remarkable performance across various domains, including healthcare. However, their ability to effectively represent structured non-textual data, such as the alphanumeric medical codes used in records like ICD-10 or SNOMED-CT, is limited and has been particularly exposed in recent research. This paper examines the challenges LLMs face in processing medical codes due to the shortcomings of current tokenization methods. As a result, we introduce the UniStruct architecture to design a multimodal medical foundation model of unstructured text and structured data, which addresses these challenges by adapting subword tokenization techniques specifically for the structured medical codes. Our approach is validated through model pre-training on both an extensive internal medical database and a public repository of structured medical records. Trained on over 1 billion tokens on the internal medical database, the proposed model achieves up to a 23% improvement in evaluation metrics, with around 2% gain attributed to our proposed tokenization. Additionally, when evaluated on the EHRSHOT public benchmark with a 1/1000 fraction of the pre-training data, the UniStruct model improves performance on over 42% of the downstream tasks. Our approach not only enhances the representation and generalization capabilities of patient-centric models but also bridges a critical gap in representation learning models' ability to handle complex structured medical data, alongside unstructured text.