Recent attosecond-streaking spectroscopy experiments [A. L. Cavalieri, Nature (London) 449, 1029 (2007)10.1038/nature06229] using copropagating extreme ultraviolet (XUV) and infrared (IR) pulses of variable relative delay have measured a delay of approximately 100 attoseconds between photoelectrons emitted by a single XUV photon from localized core states and delocalized conduction-band states of a tungsten surface. We analyze the underlying XUV-photoemission-IR-streaking mechanism by combining a perturbative description of the XUV-photoemission process and the subsequent nonperturbative IR streaking of the photoelectrons. Our calculated time-resolved photoelectron spectra agree with the experiments of Cavalieri et al. and demonstrate that the observed temporal shift is caused by the interference of core-level photoelectrons that originate in different layers of the solid.