Media framing refers to the emphasis on specific aspects of perceived reality to shape how an issue is defined and understood. Its primary purpose is to shape public perceptions often in alignment with the authors' opinions and stances. However, the interaction between stance and media frame remains largely unexplored. In this work, we apply an interdisciplinary approach to conceptualize and computationally explore this interaction with internet memes on climate change. We curate CLIMATEMEMES, the first dataset of climate-change memes annotated with both stance and media frames, inspired by research in communication science. CLIMATEMEMES includes 1,184 memes sourced from 47 subreddits, enabling analysis of frame prominence over time and communities, and sheds light on the framing preferences of different stance holders. We propose two meme understanding tasks: stance detection and media frame detection. We evaluate LLaVA-NeXT and Molmo in various setups, and report the corresponding results on their LLM backbone. Human captions consistently enhance performance. Synthetic captions and human-corrected OCR also help occasionally. Our findings highlight that VLMs perform well on stance, but struggle on frames, where LLMs outperform VLMs. Finally, we analyze VLMs' limitations in handling nuanced frames and stance expressions on climate change internet memes.