Histological staining of tissue biopsies, especially hematoxylin and eosin (H&E) staining, serves as the benchmark for disease diagnosis and comprehensive clinical assessment of tissue. However, the process is laborious and time-consuming, often limiting its usage in crucial applications such as surgical margin assessment. To address these challenges, we combine an emerging 3D quantitative phase imaging technology, termed quantitative oblique back illumination microscopy (qOBM), with an unsupervised generative adversarial network pipeline to map qOBM phase images of unaltered thick tissues (i.e., label- and slide-free) to virtually stained H&E-like (vH&E) images. We demonstrate that the approach achieves high-fidelity conversions to H&E with subcellular detail using fresh tissue specimens from mouse liver, rat gliosarcoma, and human gliomas. We also show that the framework directly enables additional capabilities such as H&E-like contrast for volumetric imaging. The quality and fidelity of the vH&E images are validated using both a neural network classifier trained on real H&E images and tested on virtual H&E images, and a user study with neuropathologists. Given its simple and low-cost embodiment and ability to provide real-time feedback in vivo, this deep learning-enabled qOBM approach could enable new workflows for histopathology with the potential to significantly save time, labor, and costs in cancer screening, detection, treatment guidance, and more.