Recent advances in Large Language Models (LLMs) have raised urgent concerns about LLM-generated text authenticity, prompting regulatory demands for reliable identification mechanisms. Although watermarking offers a promising solution, existing approaches struggle to simultaneously achieve three critical requirements: text quality preservation, model-agnostic detection, and message embedding capacity, which are crucial for practical implementation. To achieve these goals, the key challenge lies in balancing the trade-off between text quality preservation and message embedding capacity. To address this challenge, we propose BiMark, a novel watermarking framework that achieves these requirements through three key innovations: (1) a bit-flip unbiased reweighting mechanism enabling model-agnostic detection, (2) a multilayer architecture enhancing detectability without compromising generation quality, and (3) an information encoding approach supporting multi-bit watermarking. Through theoretical analysis and extensive experiments, we validate that, compared to state-of-the-art multi-bit watermarking methods, BiMark achieves up to 30% higher extraction rates for short texts while maintaining text quality indicated by lower perplexity, and performs comparably to non-watermarked text on downstream tasks such as summarization and translation.