GPR full-waveform inversion (FWI) is a challenging high-resolution inversion approach for GPR data that can return simultaneously the electromagnetic wave velocity and attenuation. In recent years, crosshole GPR FWI has been applied to a wide range of applications, where it has been mostly implemented in the computationally attractive 2D domain. Thereby, the measured 3D data are converted to 2D by applying a 3D to 2D transformation that compensates for the differences in geometrical spreading and the pointe source and line source differences in 3D and 2D, respectively. This transformation function uses the first arrivals of the waves and performs well for relatively homogenous situations. However, for more complex heterogeneous structures that cause multiple (interfering) waves (e.g. high amplitude late arrivals due to a low-velocity waveguide) significant errors can occur. In order to prevent the occurrence of these errors, we replaced the 2D forward modeling part of the 2D crosshole GPR FWI with the open source finite-difference time-domain (FDTD) simulator GprMax3D (www.gprmax.com). This coupling allows us to honor the 3D wave characteristics and to avoid the 3D-2D conversion of the data. The inversion is performed for a selected plane in the 3D model, whereas the medium properties are assumed to not vary in the third perpendicular dimension. The computationally more expensive 2.5D FWI has been used to invert synthetic and experimental crosshole GPR data, and returns in both cases improved permittivity and conductivity tomograms with better data fits compared to the 2D FWI results. Similar to the 2D FWI, an initial model that returns at least half a wavelength overlap of the measured data is required for a successful convergence of inversion. Using an appropriate start model, the final 2.5D FWI converges faster with less iterations and reaches a better misfit than 2D FWI.