The hematological diagnostic of blood requires automated blood cell classification, which allows recognizing such a disorder as leukemia, anemia, and infection at an early stage. Convolutional neural networks (CNNs) are effective in the extraction of local cellular features yet have been limited in their ability to capture global contextual relationships to perform well in complex multi-class blood smear analysis due to their limitations. To overcome this drawback, the present paper suggests HemoNet-B0, which is a lightweight hybrid CNNTransformer network, taking the efficient extraction of local texture and morphological features based on EfficientNet-B0 and a compact Vision Transformer network to extract global contextual features in the form of neural network predictions. The suggested model will balance the classification accuracy and computational efficiency to the advantage. HemoNet-B0 is tested on publicly available peripheral blood cell data consisting of eight diagnostic classes under three-fold cross-validation. The experimental findings show that the proposed model attains an accuracy, precision, and a recall of 98.93 percent using a minimum of 5.47 million parameters, which exceeds various CNN- and transformer-based baselines. It is observed that training stability and uniform generalization happen between folds. Moreover, SHAP and LIME evaluation show that the model concentrates on clinically significant areas, which improves the interpretability of the model and aids in making clear decisions in automated hematological analysis.