The thickness of a bilayer membrane is primarily determined by the lipid tail length and partially determined by the solvent. Therefore, you should expect the membrane thickness to be the same regardless of the cup material.

You may experience a differenct membrane capacitance on cups of differing material but having the same hole size. Basically, the lipid/solvent mixture forms a torus around the edge of the hole, and this torus will be larger or smaller based on how well the solvent wets the cup.

Note: This effect affects the area of a membrane not its thickness.