The true skin is called cutis. It consists of two layers; the dermis and the epidermis.
"Undercote, or undercoat; fester under the skin (coat is "cutis")." from: Letters of Samuel Rutherford
"The cavity of the epimere disappears, and its walls form the muscle and cutis plates of the body."
Source: The Origin of Vertebrates by Walter Holbrook Gaskell