X-ray diffraction and simulation were used to characterize the morphological evolution that takes place in permalloy/silver (NiFe/Ag) multilayers as the result of thermal annealing. Auger spectroscopy, electron microscopy, resistivity and magnetoresistivity measurements were performed in order to obtain additional insight into the results. The results are consistent with the model of Ag grain boundary diffusion taking place along the columnar grains, leading to the creation of so-called 'silver bridges' between the permalloy grains. The initial stages of annealing (up to 633 K) result in formation of individual NiFe grains that leads to enhanced values of the magnetoresistivity. Annealing at higher temperatures causes the growth of relatively large Ag and NiFe agglomerates and results in breakup of the original multilayered structure.