We present a new method for probing ultrafast time-dependent currents in two-dimensional bilayer heterostructures by recording the associated emitted electromagnetic fields. This detection scheme offers direct sensitivity to the flow of charges at the atomic-scale and enables a real-time non-contact probe for investigating ultrafast charge transfer processes at molecular interfaces. Upon photo-excitation with above-gap photons, here we observe a burst of electromagnetic radiation from a bilayer transition metal dichalcogenide (TMDC) heterostructure (e.g., MoS2 on WS2) having a Type-II band alignment. The emitted electric field transients encode information about the charge transfer within this heterostructure. We detect the emitted electromagnetic fields via phase-sensitive free-space electro-optic sampling and show that these fields have spectral content at the terahertz (THz) frequency range. The polarity of the emitted field reflects the direction of the charge transfer and the polarity is reversed as the order of the monolayers within the heterostructure is inverted. Importantly, through analyzing the emitted field transients, we find that the charge transfer proceeds at an ultrafast rate (~100 fs) indicating a remarkable efficiency for the charge separation across these atomic-scale bilayers. Therefore, Type-II TMDC heterostructures could enable broadband THz emitters owing to the efficient and ultrafast charge transfer observed. Moreover, the detection of the emitted electromagnetic radiation presented here can be applied to a broad range of materials employed for solar light-harvesting and photo-catalysis to probe charge transfer processes at the atomic-scale in real-time with high time resolution.