How thick is a white eggshell membrane?

Well, it's not really thin and working with them tells you that they have some definite thickness. Perhaps to measure them, soak a raw egg in white vinegar for about 24 hours and then wash it off. You should end up with a pliable semitransparent egg membrane enclosing the insides of the egg. I would think you could get a rough idea by using a caliper to measure the thickness after you rupture the membrane. Good Luck!