Melanoma is the deadliest form of skin cancer, and its depth of invasion (DoI) is an important factor used by pathologist for grading the severity of skin disease. In this paper, we propose an automated technique for measuring melanoma DoI in MART1 stained skin histopathological images. The proposed technique first segments skin melanoma areas based on image color features. The skin epidermis is then segmented by a multi-thresholding method. After that, the skin granular layer is identified based on Bayesian classification of segmented epidermis pixels. Finally, the melanoma DoI is computed using a Hausdorff distance measure. Experiments on 28 skin biopsy images show that the proposed technique provides a superior performance in measuring the melanoma DoI than two closely related works.