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Recent advancements in Deep Learning models hold the potential to revolutionize the automated analysis of EEG data for early and accurate diagnosis of epileptic seizures. This paper introduces an interpretable hybrid model, integrating Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks, with a primary emphasis on two-class epileptic seizure classification. Extensive evaluations across diverse datasets establish the model's resilience and effectiveness. Notably, in the CHB-MIT dataset, the model achieves an average validation accuracy of 92.8 %, an average area under the curve of 93 %, an average specificity of 90.3 %, an average sensitivity of 95 %, an F1-score of 94 %, and an MCC of 88.2 %. In the Siena dataset, an average validation accuracy of 92.7 %, an average area under the curve of 93 %, an average specificity of 84 %, an average sensitivity of 91 %, an F1-score of 92.5 %, and an MCC of 85 % are maintained. In the Helsinki dataset, the model attains an average validation accuracy of 86.4 %, accompanied by an average area under the curve of 86 %, an average specificity of 84 %, a sensitivity of 88 %, an F1-score of 87.8 %, and an MCC of 75.3 %. Furthermore, the proposed model provides a post-hoc explainer utilizing the Shapley Additive Explanations (SHAP) method, specifically the SHAP Gradient Explainer that interprets the predictive model by providing two forms of explanation: (i) Event-wise explanations, elucidating why particular EEG data segments are classified as seizures or non-seizure events, and (ii) Patient-wise explanations that precisely pinpoint the brain lobe and hemisphere responsible for the seizure's origin. The explainer's efficacy is meticulously assessed using ground truth data, yielding localization and lateralization accuracy scores of 85.43 % for the CHB-MIT dataset, 86 % for the Siena dataset, and 79.4 % for the Helsinki dataset. This research contributes to the advancement of the responsible and trustworthy use of Artificial Intelligence in seizure vs. non-seizure EEG classification and interpretation, delivering both precise classification and in-depth explanations. [ABSTRACT FROM AUTHOR]