Convenient tracking of food intake is essential for linking diet to health, enabling personalised nutrition guidance, early metabolic risk detection, and prevention of chronic disease. Recent wearable sensing advances have begun to automate eating monitoring. However, these systems largely focus on detecting when users eat and only weakly address what they eat. In particular, state-of-the-art solutions typically cover only a narrow range of foods or textures and rely on strong assumptions about individual eating behaviour. Moreover, they overlook the nutritional implications most relevant to end users, limiting their usefulness for real-world dietary guidance. In this paper, we present NutriEar, an in-ear audio sensing system for nutrition-aware classification of food intake from chewing sounds. Rather than recognising arbitrary food types, NutriEar maps in-ear acoustics to an eight-class nutrition-texture taxonomy grounded in food science, capturing both dominant macronutrient role and mechanical texture. NutriEar records in-ear audio during eating, segments chewing events, and derives a hybrid representation combining engineered acoustic features with learned embeddings from supervised contrastive learning, enabling a compact nutrition-aware classification pipeline. Evaluation on a dataset collected from 15 users consuming over 30 food types under varied eating conditions shows that NutriEar achieves 80.18% average leave-one-subject-out (LOSO) accuracy and outperforms state-of-the-art baselines. These results highlight the untapped potential of earable audio sensing as a practical pathway toward everyday dietary monitoring with meaningful nutritional insights.