The white part of the eye is called the sclera, which is covered by a transparent, onion skin like membrane called the conjunctiva. The conjunctiva joins the cornea at the limbus, the very edge of the cornea. The cornea is a basically a clear lens that gives the eye 70% of it's focusing power. The iris, or color part of the eye, sits behind the cornea in what is called the anterior chamber.
The only transparent parts of the eye are the cornea and conjunctiva. The lens and vitreous are translucent.
Since I was in ophthalmology for 16 years, I have several hubs on the eye if you'd like more information.