Plasma catalysis, biomedical applications or atomic layer deposition at atmospheric pressure all make use of non-thermal plasmas in contact with a wide variety of surfaces. As the presence of a target (substrate) has been shown to modify the plasma in addition to the plasma modifying the target, it is reasonable to describe and study the plasma-surface as one system. This work shows how the presence of dielectric and metallic targets influences a kHz AC-driven discharge in a He plasma jet. Next to bringing the absolute values of the axial electric field along the plume of the jet, the presence of the surface has been shown to significantly elongate both the plume and the electric field profile. In addition, when a dielectric target is placed closer than the maximum length of the freely expanding jet, the electric field profile is enhanced only in the vicinity of the dielectric, typically between 0.3 and 2 mm above the target surface. The maximum measured relative increase is 31%, for 1000 SCCM flow with the target at 7 mm distance, when the electric field increased from 14.1 kV cm−1 for the freely expanding jet to 32.6 kV cm−1 when the jet was impinging on glass. Finally, a grounded metallic target enhances the electric field compared to the glass target only within a very thin layer just above the surface, typically about 0.2 mm. The highest measured electric field was 40.1 kV cm−1 at a grounded metallic target 12 mm away from the nozzle, for 1000 SCCM of helium flow. The discussion on the effects of the flow on the electric field profile are supported by the visualization of the flow. The discussion brings, among other, the comparison of properties between the 30 kHz AC-driven system and the 5 kHz pulsed jet.