Assessing the state of mixing on the molecular scale in soft solids is challenging. Concentrated solutions of micelles formed by self-assembly of polystyrene-block-poly(ethylene-alt-propylene) (PS-PEP) diblock copolymers in squalane (C30H62) adopt a body-centered cubic (bcc) lattice, with glassy PS cores. Utilizing small-angle neutron scattering (SANS) and isotopic labeling (1H and 2H (D) polystyrene blocks) in a contrast-matching solvent (a mixture of squalane and perdeuterated squalane), we demonstrate quantitatively the remarkable fact that a commercial mixer can create completely random mixtures of micelles with either normal, PS(H), or deuterium-labeled, PS(D), cores on a well-defined bcc lattice. The resulting SANS intensity is quantitatively modeled by the form factor of a single spherical core. These results demonstrate both the possibility of achieving complete nanoscale mixing in a soft solid and the use of SANS to quantify the randomness.