Supervised virtual staining methods achieve high accuracy when trained on large-scale paired data. However, paired H&E-to-IHC images are extremely scarce. Furthermore, staining variations caused by differences in staining protocols and scanning equipment introduce irrelevant discrepancies that further hinder model performance. The scarcity of paired data and staining variations across institutions represent two major challenges in virtual staining. To address these issues, we propose a staining variability-aware semi-supervised framework. The semi-supervised approach leverages a small number of paired H&E-IHC image pairs along with more unlabeled H&E images to enhance model performance. Furthermore, the staining variability-aware perturbation method simulates staining differences across institutions and staining batches. These two strategies improve the robustness, generalizability, and overall staining consistency of the model. Our method further unlocks the potential of supervised approaches when paired data is limited. Experimental results demonstrate that our method significantly improves virtual staining performance. The code will be available.