Recently, the interest in the induced polarization (IP) phenomenon in airborne time-domain electromagnetic (ATEM) data has increased considerably. IP may affect the ATEM data significantly and mask underlying geologic structures. To simulate 2D airborne IP data, a 2D finite-element forward-modeling algorithm has been developed with the dispersive conductivity described by the well-known Cole-Cole model. We verify our algorithm by comparison with the 1D solution of the AarhusInv code. Two-dimensional forward responses on six synthetic models, mimicking archetypal 2D conductive and chargeable anomalies, have been generated, and the results indicate that 2D IP affects the data significantly. Differences between the 2D IP responses and the 1D IP responses are evident above the 2D anomalies and at their edges. These differences are similar to what is found when comparing 2D and 1D forward responses over conductive 2D anomalies without considering IP. We evaluate an effective robust inversion scheme to recover the 2D IP parameters using the 1D laterally constrained inversion (LCI) scheme. The inversion of the synthetic data using the robust scheme indicates that not only can the IP parameters be recovered, but also the IP inversions can provide more accurate resistivity sections than a resistivity-only inversion, in terms of resistivity values and anomaly thickness/depth. The field example from Hope Bay area in Canada is even more valuable, considering that part of the profile consists of only negative data, which cannot be inverted with a resistivity-only scheme. Furthermore, the edge effects at the anomaly boundaries are less pronounced in the IP parameters than in the resistivity parameter on the synthetic models with more conductive backgrounds.