The resistive touch screen works by having two layers of electrically conductive material near each other, but not quite touching. When you press your finger on it, the two conductive layers of material touch and some analog readings can be made in order to determine where the two layers are being touched. Essentially, the layers make two voltage dividers, one in the horizontal direction and one in the vertical direction. One direction is measured and then the other. This gives X and Y coordinates. If you place a sheet of glass over the two conductive layers, then you won't be able to push on the layers to make them come into contact with each other. You might be able to get by with a clear polyester type sheet over the resistive touch screen, but I would imagine that it would reduce resolution so you'd have to make your "buttons" bigger on the display.
Someone else should elaborate on the capacitive touch screen. I've looked into them just enough to know that I'd rather use a resistive touch screen on my projects than a capacitive touch screen. However, in general, the capacitive touch screen will work through sheets of protective material, but the thinner the better.
Another alternative would be to place a sheet of glass between the LCD and the touchscreen. This introduces other problems such as not pressing exactly where you think you're pressing due to the angle and thickness of the glass.