Contrast-variation small-angle neutron scattering (CV-SANS) is an excellent way to determine the structure of complex, hierarchical colloids, including self-assembled biological systems. In these experiments, the scattering length density of solvents is changed (by varying the ratio of water or H2O and heavy water or D2O) to highlight or mask scattering from different components in the system. This approach has been used with synthetic colloids, but it is also increasingly being used in the biological and food sciences. Perhaps the most studied food colloid is the "casein micelle", a self-assembled nanometer-scale colloid of the structure-forming casein protein in milk. CV-SANS data available in the literature are typically analyzed using approximations, which may be invalid for casein micelles, as they have been shown to be sticky spheres. To assess the applicability of this approximate approach, a comprehensive set of CV-SANS data from casein micelles in diluted milk was reanalyzed using a model-based approach, where the casein micelles were formally treated as interacting spheres. In general, the conclusions of the previous study are reproduced, but this new approach makes it more straightforward to distinguish the different components in milk and can be applied to any dairy sample with known form of interparticle interactions, which offers the possibility of studying semi-deuterated milk at its native concentration.