Code-mixed text—where multiple languages are used within the same utterance—is increasingly common in both spoken and written communication. However, it presents significant challenges for machine learning models due to the interplay of distinct grammatical structures, effectively forming a hybrid language. While fine-tuning large language models (LLMs) such as GPT-3, or Llama-3 on code-mixed data has led to performance improvements, these models still lag behind their monolingual counterparts and incur high computational costs due to the large number of trainable parameters.In this paper, we focus on the task of sentiment detection in code-mixed text and propose a Hybrid Language Model (HLM) that combines a multilingual encoder (e.g., mBERT) with a lightweight decoder (e.g., Sarvam-1) (3B parameters). Despite having significantly fewer trainable parameters, HLM achieves sentiment classification performance comparable to that of fine-tuned Large Language Models (LLMs) (> 7B parameters). Furthermore, our results demonstrate that HLM significantly outperforms models trained individually, underscoring its effectiveness for low-resource, code-mixed sentiment analysis.