This paper presents a novel approach for unsupervised domain adaptation (UDA) targeting H&E stained histology images. Existing adversarial domain adaptation methods may not effectively align different domains of multimodal distributions associated with classification problems. The objective is to enhance domain alignment and reduce domain shifts between these domains by leveraging their unique characteristics. Our approach proposes a novel loss function along with carefully selected existing loss functions tailored to address the challenges specific to histology images. This loss combination not only makes the model accurate and robust but also faster in terms of training convergence. We specifically focus on leveraging histology-specific features, such as tissue structure and cell morphology, to enhance adaptation performance in the histology domain. The proposed method is extensively evaluated in accuracy, robustness, and generalization, surpassing state-of-the-art techniques for histology images. We conducted extensive experiments on the FHIST dataset and the results show that our proposed method - Domain Adaptive Learning (DAL) significantly surpasses the ViT-based and CNN-based SoTA methods by 1.41% and 6.56% respectively.