Computer-aided diagnostic has become a thriving research area in recent years, namely on the identification of skin lesions such as melanoma. This work presents a novel approach to this field by exploiting the 3D characteristics of the skin lesion surface, advancing beyond common features such as, shape, colour, and texture, extracted from dermoscopic RGB images. To this end, a relevant set of features was investigated to obtain 3D skin lesion characteristics from images with depth information. These features were used to train a Bag-of-Features model to distinguish between malignant and benign lesions, also discriminating melanoma from all other lesion types. Despite the large class imbalance, often present in medical image datasets, the feature set achieved a top accuracy of 73.08%, comprising 75.00% sensitivity and 66.67% specificity when classifying between malignant and benign lesions, and 88.46% accuracy (100.00% sensitivity and 86.96% specificity) when discriminating melanoma from all other lesion images, using only depth information. The achieved experimental results indicate the existence of relevant discriminative characteristics in the 3D surface of skin lesions which allow the improvement of existing classification methods based on 2D image characteristics only.