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We describe a general method for the quantitative determination of the interlayer mass transport in epitaxial growth. Through measurement of the nucleation rate on top of islands as a function of island size and temperature, the additional barrier for an adatom to descend the step edge Delta E(s) can be determined with high accuracy. This approach is applied to the growth of Ag on the (111) surfaces of Ag and Pt. In the homoepitaxial system, the barrier is found to be Delta E(s) = 120 +/- 15 meV, whereas in the heteroepitaxial case it is substantially lowered, Delta E(s) = 30 +/- 5 meV.