The rapid growth of machine learning (ML) systems necessitates a more comprehensive evaluation of their environmental impact, particularly their carbon footprint, which comprises operational carbon from training and inference execution and embodied carbon from hardware manufacturing and its entire life-cycle. Despite the increasing importance of embodied emissions, there is a lack of tools and frameworks to holistically quantify and optimize the total carbon footprint of ML systems. To address this, we propose CATransformers, a carbon-aware architecture search framework that enables sustainability-driven co-optimization of ML models and hardware architectures. By incorporating both operational and embodied carbon metrics into early design space exploration of domain-specific hardware accelerators, CATransformers demonstrates that optimizing for carbon yields design choices distinct from those optimized solely for latency or energy efficiency. We apply our framework to multi-modal CLIP-based models, producing CarbonCLIP, a family of CLIP models achieving up to 17% reduction in total carbon emissions while maintaining accuracy and latency compared to state-of-the-art edge small CLIP baselines. This work underscores the need for holistic optimization methods to design high-performance, environmentally sustainable AI systems.