Which surfaces contain no epithelial tissues and which epithelial tissues are vascular?
I think you're talking about two different things.  I assume Rafique is referring to vascularized epithelium, but user4693 is referring to vascular epithelium.  Although the terminology is very similar, the difference is important.

vascular epithelium = endothelium of a blood or lymphatic vessel.

vascularized epithelium = epithelium with a blood supply, meaning that small vessels invade the epithelium (pass between epithelial cells) rather than simply occurring in the underlying basement membrane or connective tissue.

Most epithelia are avascular (lack blood vessels).  As far as I know the only vascularized epithelium in humans is found in the inner ear (1).  I've been told that the lips have vascularized epithelium (which is why they appear reddish), but I don't completely trust that source and I cannot find anything online to support it.

Also, some pathological conditions can cause vascularization of certain epithelia, like the cornea (2).