The surface structure of Cu(100) modified by chloride and iodide has been studied in an electrochemical environment by means of in-situ scanning tunneling microscopy in combination with in-situ surface X-ray diffraction with a particular focus on adsorbate and potential dependent surface relaxation phenomena. For positive potentials close to the on-set of the copper dissolution reaction, the X-ray data disclose an extraordinarily large Cu-Cl bond length of 2.61 angstrom for the c(2 x 2)-Cl phase. This finding points to a largely ionic character of the Cu-Cl interaction at the Cu(100) surface, with chloride particles likely to retain their full charge upon adsorption. Together with the positive surface charging at these high potentials, this ionic Cu-Cl bond drives the observed 2.2% outward relaxation between the first two copper layers. These results indicate that the bond between the first and the second copper layer is significantly weakened which appears as the crucial prerequisite for the high surface mobility of copper-chloride species under electrochemical annealing conditions at these high potentials. With 2.51 angstrom the Cu-I bond is 4% shorter than the Cu-Cl bond implying that the nature of the Cu-I bond is mainly covalent. Accordingly, we observe a significant inward relaxation of the top Cu layers upon substituting chloride by iodide at the same electrode potential, which suggests that the iodide adsorption involves charge transfer from the halide to the copper substrate.