Monte Carlo (MC) codes are useful tools to simulate the complex processes of proton beam interactions with matter. In proton therapy, nuclear reactions influence the dose distribution. Therefore, the validation of nuclear models adopted in MC codes is a critical requisite for their use in this field. A simple integral test can be performed using a multi-layer Faraday cup (MLFC). This method allows separation of the nuclear and atomic interaction processes, which are responsible for secondary particle emission and the finite primary proton range, respectively. In this work, the propagation of 160 MeV protons stopping in two MLFCs made of polyethylene and copper has been simulated by the FLUKA MC code. The calculations have been performed with and without secondary electron emission and transport, as well as charge sharing in the dielectric layers. Previous results with other codes neglected those two effects. The impact of this approximation has been investigated and found to be relevant only in the proximity of the Bragg peak. Longitudinal charge distributions computed with FLUKA with both approaches have been compared with experimental data from the literature. Moreover, the contribution of different processes to the measurable signal has been addressed. A thorough analysis of the results has demonstrated that the nuclear and electromagnetic models of FLUKA reproduce the two sets of experimental data reasonably well.