In the last years, artificial intelligence (AI) in clinical decision support systems (CDSS) played a key role in harnessing machine learning and deep learning architectures. Despite their promising capabilities, the lack of transparency and explainability of AI models poses significant challenges, particularly in medical contexts where reliability is a mandatory aspect. Achieving transparency without compromising predictive accuracy remains a key challenge. This paper presents a novel method, namely Rad4XCNN, to enhance the predictive power of CNN-derived features with the interpretability inherent in radiomic features. Rad4XCNN diverges from conventional methods based on saliency map, by associating intelligible meaning to CNN-derived features by means of Radiomics, offering new perspectives on explanation methods beyond visualization maps. Using a breast cancer classification task as a case study, we evaluated Rad4XCNN on ultrasound imaging datasets, including an online dataset and two in-house datasets for internal and external validation. Some key results are: i) CNN-derived features guarantee more robust accuracy when compared against ViT-derived and radiomic features; ii) conventional visualization map methods for explanation present several pitfalls; iii) Rad4XCNN does not sacrifice model accuracy for their explainability; iv) Rad4XCNN provides global explanation insights enabling the physician to analyze the model outputs and findings. In addition, we highlight the importance of integrating interpretability into AI models for enhanced trust and adoption in clinical practice, emphasizing how our method can mitigate some concerns related to explainable AI methods.