An energy discriminating detector for dual-energy radiography can be configured as a two-layer sandwich, where the mean energy of photons detected by the two layers differs. To characterize the quantum noise of such a detector, the noise covariance between the two layers must be known in addition to the noise variance in each layer. A theory is presented which permits the calculation of the noise covariance, and it is found to be negligibly small. Experimental results, based on measurements with a Nal sandwich detector and an isotope gamma ray source, are reported and shown to confirm the theory. The quantum noise in each layer is independent and Poisson. © 1989, American Association of Physicists in Medicine. All rights reserved.