Parameter-efficient fine-tuning of pre-trained codecs is a promising direction in image compression for human and machine vision. While most existing works have primarily focused on tuning the feature structure within the encoder-decoder backbones, the adaptation of the statistical semantics within the entropy model has received limited attention despite its function of predicting the probability distribution of latent features. Our analysis reveals that naive adapter insertion into the entropy model can lead to suboptimal outcomes, underscoring that the effectiveness of adapter-based tuning depends critically on the coordination between adapter type and placement across the compression pipeline. Therefore, we introduce Structure-Semantics Co-Tuning (S2-CoT), a novel framework that achieves this coordination via two specialized, synergistic adapters: the Structural Fidelity Adapter (SFA) and the Semantic Context Adapter (SCA). SFA is integrated into the encoder-decoder to preserve high-fidelity representations by dynamically fusing spatial and frequency information; meanwhile, the SCA adapts the entropy model to align with SFA-tuned features by refining the channel context for more efficient statistical coding. Through joint optimization, S2-CoT turns potential performance degradation into synergistic gains, achieving state-of-the-art results across four diverse base codecs with only a small fraction of trainable parameters, closely matching full fine-tuning performance. Code is available at https://github.com/Brock-bit4/S2-CoT.