The conjunctiva lines the inside of the eyelids and covers the sclera (white part of the eye).It is composed of non-keratinized, stratified columnar epithelium with goblet cells, and also stratified columnar epithelium.yperaemia of the superficial blood vessels of the conjunctiva. The conjunctiva lines the inside of the eyelids and covers the sclera (white part of the eye). It is composed of non-keratinized, stratified columnar epithelium with goblet cells, and also stratified columnar epithelium.