Chain-of-thought (CoT) reasoning has proven effective for enhancing problem-solving in large language models. However, when applied to multimodal LLMs (MLLMs), existing CoT approaches suffer from a fundamental limitation: they perform reasoning entirely in text without accessing visual features during the reasoning process. After initial visual encoding, image information becomes inaccessible, forcing models to reason based solely on whatever was captured in the initial description, which forms a `vision-blind reasoning' paradigm that limits fine-grained visual extraction, error verification, and adaptive attention. We propose Text-Visual Interleaved Chain-of-Thought (TVI-CoT), a framework that enables explicit interleaving of textual reasoning and visual feature access through learnable control tokens <THINK>, <LOOK> and <ANSWER>. These tokens allow dynamic switching between reasoning and visual grounding, attending to relevant image regions conditioned on the evolving reasoning state. Experiments on eight benchmarks demonstrate state-of-the-art results among MLLM-based CoT methods and notable performance boost compared to the baseline: +6.1% on MMMU, +3.8% on MathVerse, +3.4% on MathVista, and +3.4% on ScienceQA. Code is available at https://github.com/hulianyuyy/TVI-CoT.