Supervised speech enhancement has gained significantly from recent advancements in neural networks, especially due to their ability to non-linearly fit the diverse representations of target speech, such as waveform or spectrum. However, these direct-fitting solutions continue to face challenges with degraded speech and residual noise in hearing evaluations. By bridging the speech enhancement and the Information Bottleneck principle in this letter, we rethink a universal plug-and-play strategy and propose a Refining Underlying Information framework called RUI to rise to the challenges both in theory and practice. Specifically, we first transform the objective of speech enhancement into an incremental convergence problem of mutual information between comprehensive speech characteristics and individual speech characteristics, e.g., spectral and acoustic characteristics. By doing so, compared with the existing direct-fitting solutions, the underlying information stems from the conditional entropy of acoustic characteristic given spectral characteristics. Therefore, we design a dual-path multiple refinement iterator based on the chain rule of entropy to refine this underlying information for further approximating target speech. Experimental results on DNS-Challenge dataset show that our solution consistently improves 0.3+ PESQ score over baselines, with only additional 1.18 M parameters. The source code is available at https://github.com/caoruitju/RUI_SE.