In the context of leukemia diagnosis, the morphology of white blood cells plays a crucial role in the diagnostic process. The use of an automated framework is highly advantageous, as the diagnostic outcome can be influenced by the subjective experience of the individual making the diagnosis. To facilitate this process, blood smear slides are examined under a microscope, and a diagnosis is made based on the observed morphology. Usually deep learning frameworks are used, and potential accuracies and other metrics are obtained. These frameworks require a large amount of dataset images to achieve maximum accuracy. As leukemia is a rare disease, it has the datasets with limited-sized images. Hence, to overcome this limitation, a hybrid framework is introduced in this study. A customized Convolutional Neural Network is utilized with Support Vector Machine. The performance of this model is measured by the accuracy metric, showing an improvement from 78.33% to 91.67% by utilizing CNN-SVM against the CNN alone. Moreover, in medical diagnosis, the ability to understand and interpret the decisions made by automated frameworks is crucial. As a result, the commercial utilization of these frameworks is not widely embraced. To address this, there has been a growing emphasis on the explainability and interpretability of classifiers, particularly in indicating the specific reasons behind a decision, such as distinguishing between infected and normal cases. In our experiment, we have incorporated the widely used explainable AI (XAI) framework called Local-interpretable-model-agnostic-explanations (LIME) to interpret the performance of the classifier. This approach aims to shed light on the underlying factors influencing the classifier's decision-making process.