Virtual staining aims to computationally generate target-stained histopathological images while reducing the cost and time associated with conventional staining procedures. However, existing methods rely predominantly on strictly paired and accurately registered training data, which are difficult and expensive to obtain in routine practice. To reduce this dependence, we propose a stable semi-supervised virtual staining framework that jointly exploits both limited paired data and abundant unpaired source images. Directly incorporating unpaired images is challenging because their generated results lack corresponding targets for supervision, potentially leading to unrealistic staining, morphological degradation, or even training collapse. To obtain reliable supervision from these images, Hessian-derived morphology preservation extracts structural cues from each source image and constrains the generated output to retain tissue morphology. Histopathological realism constraints further guide the output toward plausible target-stain characteristics, preventing the source-derived structural supervision from degenerating into contour enhancement or simple color transformation. Together, the two components suppress structural and appearance drift, stabilize semi-supervised stain translation, and promote the preservation of diagnostically relevant information. Extensive experiments on H&E-to-IHC translation for Ki67 and HER2, as well as FFPE-to-H&E translation, demonstrate consistent improvements in image quality, morphology preservation, robustness, and downstream diagnostic performance. Code will be available.

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