We present our centimeter wavelength (1.4, 2.3 and 4.8 GHz) light curves of the afterglow of GRB 030329, which were obtained with the Westerbork Synthesis Radio Telescope. Modeling the data according to a collimated afterglow results in a jet-break time of 10 days. This is in accordance with earlier results obtained at higher radio frequencies. However, with respect to the afterglow model, some additional flux at the lower frequencies is present when these light curves reach their maximum after 40-80 days. We show that this additional flux can be modeled with two or more components with progressively later jet breaks. From these results we infer that the jet is in fact a structured or a layered jet, where the ejecta with lower Lorentz factors produce additional flux that becomes visible at late times in the lowest frequency bands. We show that a transition to non-relativistic expansion of the fireball at late times can also account for the observed flux excess, except for the lowest frequency (1.4 GHz) data.