Segmentation and classification of nuclei of various cell types in histology images is a fundamental task in the emerging area of computational pathology (CPath). Deep Learning (DL) methods tend to perform well but generally require large annotated datasets, which are time-consuming and costly to obtain. Semi-supervised learning (SSL) can help mitigate this challenge by exploiting a large amount of unlabeled data for model training alleviating the need for large annotated data. However, SSL models may exhibit poor generalization due to overly reliance on context resulting in a loss of self-awareness. In this paper, we propose a semi-supervised method that learns robust features from both labeled and unlabeled images. Enforces context-aware cross-consistency training in an unsupervised manner. The proposed model incorporates context-awareness consistency by contrasting pairs of overlapping images in a pixel-wise manner from different contexts resulting in robust and consistent context-aware features. Additionally, to improve the prediction confidence, cross-consistency regularization, and entropy minimization are employed on the unlabeled data, as shown by extensive comparative evaluation on a publicly available MoNuSeg dataset.