Three-dimensional (3D) histopathology of unprocessed tissues has the potential to transform disease management by enabling volumetric characterization of tissue microarchitecture and in-vivo assessment. Back-illumination Interference Tomography (BIT) is a new phase microscopy technology that provides rapid, non-destructive volumetric imaging of unprocessed tissues. However, translating BIT volumes into clinically interpretable H&E images remains challenging, particularly due to shift-variant contrast and the absence of quantitative validation benchmarks. We introduce HistoBIT3D, the first voxel-wise paired BIT and fluorescence-labeled nuclei dataset, enabling quantitative evaluation of structural preservation in unsupervised virtual staining against ground-truth nuclear distributions. Using this dataset, we present a novel virtual staining framework that translates BIT volumes with shift-variant contrast into realistic H&E volumes by leveraging bidirectional multiscale content consistency and cross-domain style reuse to enhance structural fidelity and perceptual realism. Our method achieves state-of-the-art realism metrics while significantly improving 3D nuclei segmentation accuracy and boundary preservation under zero-shot Cellpose evaluation. Together, these contributions establish a quantitatively validated, structurally faithful, and scalable pipeline for 3D virtual H&E staining, advancing the paradigm of slide-free, volumetric computational histopathology. Our data and code are available at: https://github.com/aasong113/HistoBIT3D_VirtualStaining.