We investigate the stabilization of air-water interfaces by mixtures of negatively charged latex particles (sulfate polystyrene) and cationic surfactants (alkyl trimethylammonium bromides). First we report results concerning the binding of surfactant molecules to the latex particles. As the surfactant concentration increases, the charge of the particles reverses, from negative to positive, because C(n)TAB first binds electrostatically to the latex particles and then through hydrophobic interaction with the monolayer already adsorbed on the particles as well as directly with the hydrophobic surface of the latex. Over a large range of surfactant concentrations around the charge inversion, a strong flocculation is observed and 100 mu m large aggregates form in the suspension. Unlike previous studies published on mixtures of inorganic particles with oppositely charged surfactants, we show that we can vary the sign of the zeta potential of the particles without changing the contact angle of the particles over a large range of surfactant concentrations. Indeed, the latex particles that we study are more hydrophobic than inorganic particles, hence adding moderate concentrations of the surfactant results in a weak variation of the contact angle while the charge of the particles can be reversed. This enables decoupling of the effect of zeta potential and contact angle on the interfacial properties of the mixtures. Our study shows that the contact angle and the charge of the particles are not sufficient parameters to control the foam properties, and the key-parameters are the flocculation state and the shear energy applied to produce the foam. Indeed, flocculated samples, whatever the sign of the zeta potential, enable production of a stable armour at the interface. The large aggregates do not adsorb spontaneously at the interface because of their large size, however when a large shear energy is used to produce the foam very stable foam is obtained, where particles are trapped at interfaces. We suggest that the large aggregates may be broken during shear and may reform at the interface to form a solid armour. A simple calculation taking into account the adsorption dynamics of the aggregates as a function of their size is consistent with this hypothesis.