With the aid of certain symmetry properties of the elementary transfer matrices of acoustic and electromagnetic field vectors in single layers of absorbing materials, we derive the transformation properties of the system transfer matrices of bonded stacks of absorbing layers under the operation of reversal of the direction of incident radiation. While writing the energy transmission coefficients in such a way that the system transfer matrices appear explicitly, we apply their transformation properties to show that under certain circumstances these coefficients are invariant with respect to front and back surface illumination.