Final answer:
The multilayered epithelium with cuboidal basal cells and flat cells at its surface is classified as stratified squamous.
Step-by-step explanation:
The epithelium you are describing is classified as stratified squamous. This classification is because the epithelium has multiple layers of cells (stratified), and the most apical cells (those on the surface) are flat (squamous). The fact that the basal cells are cuboidal indicates that the tissue can retain some capacity for cell division and regeneration, typical of stratified epithelia. Notably, stratified squamous epithelium is known for providing protection from abrasion, which aligns with the presence of the flat squamous cells on the surface layer.