The inner surfaces of the eyelids and part of the surface of the eyeball are covered with a very odd form of stratified epithelium, the conjunctiva. The tarsal conjunctiva is on the lids; the bulbar conjunctiva on the eyeball. The two areas meet at a point of convergence/reflection deep in the pocket over which the eyelids close.
This low power view of the eye shows both the tarsal and bulbar conjunctiva,
and the point at which the two are continuous. Note that at the cornea, the
bulbar conjunctival epithelium transitions to the stratified squamous form
covering the outer surface of the cornea, and at the mucocutaneous junction of
the eyelid, the tarsal conjunctiva merges with and is replaced by the
stratified squamous cells of the integument.
Here's a closer view of the conjunctival epithelium. It really is stratified
columnar and it really does contain large and actively secretory goblet cells. Definitely a different form of "covering and lining" epithelium!
The CT underlying this epithelium is very rich in blood vessels. Materials inserted into the conjunctival space sometimes can diffuse across the moist epithelium into the blood very easily. This can actually serve as a route for administration of drugs. For example, a few crystals of apomorphine placed into the conjunctival space of a dog will induce vomiting within minutes, thanks to rapid absorption into the blood. Other drugs can be administered this way as well.
As you might expect, this warm, moist, well-vascularized region is also prone to infection. If the anti-bacterial action of the tears doesn't keep the infectious agents to which the eye is exposed in check, an inflammation of this lining—conjunctivitis—will be the result.
Monkey eye; H&E stain, paraffin section; 40x and 400x