As deep learning is widely used in the radiology field, the explainability of Artificial Intelligence (AI) models is becoming increasingly essential to gain clinicians' trust when using the models for diagnosis. In this research, three experiment sets were conducted with a U-Net architecture to improve the disease classification performance while enhancing the heatmaps corresponding to the model's focus through incorporating heatmap generators during training. All experiments used the dataset that contained chest radiographs, associated labels from one of the three conditions ["normal", "congestive heart failure (CHF)", and "pneumonia"], and numerical information regarding a radiologist's eye-gaze coordinates on the images. The paper that introduced this dataset developed a U-Net model, which was treated as the baseline model for this research, to show how the eye-gaze data can be used in multi-modal training for explainability improvement and disease classification. To compare the classification performances among this research's three experiment sets and the baseline model, the 95% confidence intervals (CI) of the area under the receiver operating characteristic curve (AUC) were measured. The best method achieved an AUC of 0.913 with a 95% CI of [0.860, 0.966]. "Pneumonia" and "CHF" classes, which the baseline model struggled the most to classify, had the greatest improvements, resulting in AUCs of 0.859 with a 95% CI of [0.732, 0.957] and 0.962 with a 95% CI of [0.933, 0.989], respectively. The decoder of the U-Net for the best-performing proposed method generated heatmaps that highlight the determining image parts in model classifications. These predicted heatmaps, which can be used for the explainability of the model, also improved to align well with the radiologist's eye-gaze data. Hence, this work showed that incorporating heatmap generators and eye-gaze information into training can simultaneously improve disease classification and provide explainable visuals that align well with how the radiologist viewed the chest radiographs when making diagnosis.