Oral epithelial dysplasia (OED) is a pre-malignant histopathological diagnosis given to lesions of the oral cavity. Predicting OED grade or whether a case will transition to malignancy is critical for early detection and appropriate treatment. OED typically begins in the lower third of the epithelium before progressing upwards with grade severity, thus we have suggested that segmenting intra-epithelial layers, in addition to individual nuclei, may enable researchers to evaluate important layer-specific morphological features for grade/malignancy prediction. We present HoVer-Net+, a deep learning framework to simultaneously segment (and classify) nuclei and (intra-)epithelial layers in H&E stained slides from OED cases. The proposed architecture consists of an encoder branch and four decoder branches for simultaneous instance segmentation of nuclei and semantic segmentation of the epithelial layers. We show that the proposed model achieves the state-of-the-art (SOTA) performance in both tasks, with no additional costs when compared to previous SOTA methods for each task. To the best of our knowledge, ours is the first method for simultaneous nuclear instance segmentation and semantic tissue segmentation, with potential for use in computational pathology for other similar simultaneous tasks and for future studies into malignancy prediction.