We model the kinematics of the high- and intermediate- velocity clouds (HVCsand IVCs) observed in absorption towards a sample of 55 Galactic halo starswith accurate distance measurements. We employ a simple model of a thick discwhose main free parameters are the gas azimuthal, radial and verticalvelocities ($v_\phi$, $v_{\rm R}$ and $v_{\rm z}$), and apply it to the data byfully accounting for the distribution of the observed features in thedistance-velocity space. We find that at least two separate components arerequired to reproduce the data. A scenario where the HVCs and the IVCs aretreated as distinct populations provides only a partial description of thedata, which suggests that a pure velocity-based separation may give a biasedvision of the gas physics at the Milky Way's disc-halo interface. Instead, thedata are best described by a combination of an inflow and an outflowcomponents, both characterised by rotation with $v_\phi$ comparable to that ofthe disc and $v_{\rm z}$ of 50-100 km/s. Features associated with the inflowappear to be diffused across the sky, while those associated with the outfloware mostly confined within a bi-cone pointing towards ($l\!=\!220^{\circ}$,$b\!=\!+40^{\circ}$) and ($l\!=\!40^{\circ}$, $b\!=\!-40^{\circ}$). Ourfindings indicate that the lower ($|z|\!\lesssim\!10$ kpc) Galactic halo ispopulated by a mixture of diffuse inflowing gas and collimated outflowingmaterial, which are likely manifestations of a galaxy-wide gas cycle triggeredby stellar feedback, that is, the galactic fountain.