An analytical expression for the scattering profiles from a disordered melt of symmetric, nonuniformly labeled A-B diblock copolymers is derived using the multicomponent random phase approximation. The expression is simple and contains one additional, temperature-independent constant that is a measure of the ensemble-averaged deviations of the scattering lengths of the two blocks from their mean values. The kind of nonuniformity considered here is a natural consequence of many of the popular synthetic routes used to obtain deuterium labeled block copolymers. Small-angle neutron-scattering experiments were conducted on a block copolymer obtained by saturating the double bonds of an anionically synthesized polydiene precursor with deuterium. The scattering data from our block copolymer in the disordered state are qualitatively inconsistent with all of the previously published theories on block copolymer thermodynamics. The data are, however, in quantitative agreement with the proposed expression. This enables a quantitative estimate of the nonuniformity of the deuterium labels in the sample. Our work also enables a new measure of the chain dimensions of block copolymers, one that is not dependent on the location of the scattering peak that arises due to the connectivity of the blocks.