In this paper, we extend the geometric particle in cell framework on dual grids to a gauge-free drift-kinetic (DK) Vlasov–Maxwell model and its coupling with the fully kinetic (FK) model. We derive a discrete action principle on dual grids for our DK model, such that the dynamical system involves only the electric and magnetic fields and not the potentials as most DK and gyrokinetic models do. This yields a macroscopic Maxwell equation including polarization and magnetization terms that can be coupled straightforwardly with a FK model.