This work focuses on the study of bulk flows accompanying the coalescence of two aqueous drops, one containing surfactant and the other surfactant-free, in silicone oils of various viscosities. It is observed that the surfactant-free drop intrudes into the surfactant-laden drop in the form of a penetrating jet whose speed increases and average radius decreases with increasing outer phase viscosity. Mixing patterns within the coalescing drops are due to the force imbalance caused by capillary pressure difference and surfactant-induced Marangoni stresses. The driving force for mixing associated with the difference in interfacial tension between the drops is considerably stronger than that related to the drop size. The long timescale mixing of the drops is driven by rapid interior convection, and the subsequent, slow, diffusive process. Three-dimensional numerical simulations show excellent qualitative and quantitative agreement with the experimental results. The implications of our results to formulation strategies of complex microstructures in practical applications are also discussed.