We have investigated by differential scanning calorimetry the thermal evolution of Cu/Mg multilayers with different modulation lengths, ranging from 7/28 to 30/120 nm. The Cu and Mg layers were grown by sequential evaporation in an electron beam deposition system. The phase identification and layer microstructure were determined by cross-section transmission electron microscopy, Rutherford backscattering, and scanning electron microscopy with focused ion beam for sample preparation. Upon heating, the intermetallic CuMg2 forms at the interfaces until coalescence is reached and thickens through a diffusion-limited process. Cross-section transmission electron microscopy observations show a distinct microstructure at the top and bottom of the as-prepared Mg layers, while no significant differences were seen in the Cu layers. We show that this effect is responsible for the observed asymmetry in the nucleation process between the Cu on Mg and the Mg on Cu interfaces. By modeling the calorimetric data we determine the role of both interfaces in the nucleation and lateral growth stages. We also show that vertical growth proceeds by grain development of the product phase, increasing significantly the roughness of the interfaces.