Due to its high sensitivity and because it does not rely on the magneto-optical response, terahertz (THz) emission spectroscopy has been used as a powerful time-resolved tool for investigating ultrafast demagnetization and spin current dynamics in nanometer-thick ferromagnetic (FM)/heavy metal (HM) heterostructures. Here, by changing the order of the conductive HM coating on the FM nanometer film, the dominant electric dipole contribution to the laser-induced THz radiation can be unraveled from the ultrafast magnetic dipole. Furthermore, to take charge equilibration into account, we separate the femtosecond laser-induced spin-to-charge converted current and the instantaneous discharging current within the illuminated area. The THz emission spectroscopy gives us direct information into the coupled spin and charge dynamics during the first moments of the light–matter interaction. Our results also open up new perspectives to manipulate and optimize the ultrafast charge current for promising high-performance and broadband THz radiation.