The primary difference between white and black plates is their reflective properties.
For luminescent assays, white plates reflect light and will maximize light output signal.
For fluorescent assays, black plates absorb light and reduce background and crosstalk.
For multiplexed luminescent and fluorescent assays, using a white plate will support maximum light output signal for the luminescent portion of the assay, but result in higher crosstalk and background for the fluorescent portion of the assay. Using a black plate in a multiplex assay will reduce fluorescent signal crosstalk and background, but will reduce the luminescence signal (you can expect to lose about 1 order of magnitude in luminescent signal using a black plate).