Low-Light Image Enhancement (LLIE) task aims at improving contrast while restoring details and textures for images captured in low-light conditions. HVI color space has made significant progress in this task by enabling precise decoupling of chrominance and luminance. However, for the interaction of chrominance and luminance branches, substantial distributional differences between the two branches prevalent in natural images limit complementary feature extraction, and luminance errors are propagated to chrominance channels through the nonlinear parameter. Furthermore, for interaction between different chrominance branches, images with large homogeneous-color regions usually exhibit weak correlation between chrominance branches due to concentrated distributions. Traditional pixel-wise losses exploit strong inter-branch correlations for co-optimization, causing gradient conflicts in weakly correlated regions. Therefore, we propose an Inter-Chrominance and Luminance Interaction (ICLR) framework including a Dual-stream Interaction Enhancement Module (DIEM) and a Covariance Correction Loss (CCL). The DIEM improves the extraction of complementary information from two dimensions, fusion and enhancement, respectively. The CCL utilizes luminance residual statistics to penalize chrominance errors and balances gradient conflicts by constraining chrominance branches covariance. Experimental results on multiple datasets show that the proposed ICLR framework outperforms state-of-the-art methods.