Venus' nightside ionosphere may be characterized by two general magnetic field geometries. Most of the ionosphere is characterized by largely horizontal fields carried over across the terminator from the dayside. However, regions of mostly vertical fields, associated with the nightside ionospheric 'holes' and connected to regions in the ionosheath where there are strong tailward fields, are also present. A magnetic potential model has been developed to describe the interface of the ionosphere, represented as an infinite slab bounded by two magnetically impermeable planes, with the tail lobes idealized as semi-infinite solenoids terminating at the ionopause. From this model, ionospheric boundary currents are generated to confine all field lines in either the flat ionosphere or the vertical tail lobe, and the field geometries are explored. Techniques for mapping this solution to a sphere and approximating it at long ranges from the transition region are discussed, and a preliminary global nightside model is offered.