We present a new empirical model of quiet-time F-region ionospheric currents and associated magnetic fields. This model is designed to accurately represent these currents and fields at low and mid latitudes. For each individual Swarm satellite, the preprocessed data is represented as a non-potential toroidal magnetic field using the Mie representation in a thin-shell and spherical harmonic expansions. This approach allows to fully separate spatial and climatological variations as well as to assess the robustness of the model with respect to both measurement errors and data sampling with local time. The obtained model describes the toroidal magnetic fields and the associated radial poloidal electric currents at two distinct altitudes in the ionosphere F region. Clear signatures of low- and mid-latitude interhemispheric field-aligned currents (IHFACs) are identified. The model reproduces well-known characteristics of the climatology of IHFACs and provides new insights, for example, on the average daily variations of IHFACs during winter in the Northern Hemisphere. It also well recovers the variations of IHFACs with longitude. The potential driving mechanisms of these variations, such as longitudinal variations of the main field and modulation by upward propagating atmospheric tides, are discussed. The new model can be used to analyze the relationship between atmospheric tides and IHFACs. It can also be used to investigate the connection between the magnetic fields and electric currents from the ionospheric E and F regions in order to improve the separation of these fields as well as our understanding of the overall ionospheric electric current system.