Using surface x-ray diffraction we have studied the geometric structure of ultrathin Pd films grown on Cu(001) at room temperature by pulsed laser deposition in the coverage regime between 0.4 and about 4 monolayers (ML). Up to about 2 ML, the interface formation is characterized by an alloying-dealloying mechanism, where Pd atoms are incorporated into the Cu substrate for less than half-filled layers, but expelled if the Pd coverage is close to a complete layer. In this case the top layer is composed of Pd. Above 2 ML, Pd agglomeration sets in characterized by Pd-rich alloy layers covered by Pd layers. Interlayer spacings linearly depend on the Pd concentration χ in the Pd_χCu_1−χ alloy layers in agreement with continuum elasticity considerations. Our results have important implications for modeling strain relaxation.