We present a theory for studying the details of the screened electron-electron interaction in fullerenes by means of the coincident electron emission upon charged particle impact. The cross sections for this process are expressed in terms of the screened electron-electron interaction and evaluated within the random-phse approximation. We performed full quantum mechanical calculations for the cross sections and obtained fair agrrement with available experiments. Furthemore, we present theoretical angular and energy-resolved cross sections to underline the wealth of information that can be gained by future experiments.