We have investigated the stability of a mixed colloidal system of sodium dodecyl sulfate (SDS) micelles and colloidal silica (Ludox TM). The colloidal silica is stably dispersed in water by virtue of its surface charge, but at SDS concentrations greater than 0.45 M the silica particles slowly aggregate. This transition is monitored with small angle neutron scattering (SANS) using a solvent contrast variation technique. Partial structure factors for the binary mixture are extracted from the SANS data using an optimization-regularization procedure. Knowledge of the partial structure factors in this asymmetric mixture (the Ludox radius is five times that of the micelles) allows us to determine the three pair interaction potentials. Model calculations for a multicomponent sticky hard sphere fluid are fitted to the experimental partial structure factors, thereby quantifying all three pair interaction potentials (which are potentials of mean force). For a fixed silica volume fraction of 0.063, attractive interactions between the silica particles increase as the volume fraction of micelles is increased from 0.021 to 0.181. The micelles interact with a screened Coulomb repulsion that decreases in strength as the micelle concentration increases. The micelle-Ludox interaction has not been previously measured, and can be modeled as a hard-sphere-charged-sphere interaction for all of the mixture compositions studied.