Despite recent medical advancements, breast cancer remains one of the most prevalent and deadly diseases among women. Although machine learning-based Computer-Aided Diagnosis (CAD) systems have shown potential to assist radiologists in analyzing medical images, the opaque nature of the best-performing CAD systems has raised concerns about their trustworthiness and interpretability. This paper proposes MT-BI-RADS, a novel explainable deep learning approach for tumor detection in Breast Ultrasound (BUS) images. The approach offers three levels of explanations to enable radiologists to comprehend the decision-making process in predicting tumor malignancy. Firstly, the proposed model outputs the BI-RADS categories used for BUS image analysis by radiologists. Secondly, the model employs multi-task learning to concurrently segment regions in images that correspond to tumors. Thirdly, the proposed approach outputs quantified contributions of each BI-RADS descriptor toward predicting the benign or malignant class using post-hoc explanations with Shapley Values.