Magnetotelluric (MT), radiomagnetotelluric (RMT), and, in particular, controlled-source audiomagnetotelluric (CSAMT) data are often heavily distorted by near-surface inhomogeneities. We developed a novel scheme to invert MT, RMT, and CSAMT data in the form of scalar or tensorial impedances and vertical magnetic transfer functions simultaneously for layer resistivities and electric and magnetic galvanic distortion parameters. The inversion scheme uses smoothness constraints to regularize layer resistivities and either Marquardt-Levenberg damping or the minimum-solution length criterion to regularize distortion parameters. A depth of investigation range is estimated by comparing layered model sections derived from first- and second-order smoothness constraints. Synthetic examples demonstrate that earth models are reconstructed properly for distorted and undistorted tensorial CSAMT data. In the inversion of scalar CSAMT data, such as the determinant impedance or individual tensor elements, the reduced number of transfer functions inevitably leads to increased ambiguity for distortion parameters. As a consequence of this ambiguity for scalar data, distortion parameters often grow over the iterations to unrealistic absolute values when regularized with the Marquardt-Levenberg scheme. Essentially, compensating relationships between terms containing electric and/or magnetic distortion are used in this growth. In a regularization with the minimum solution length criterion, the distortion parameters converge into a stable configuration after several iterations and attain reasonable values. The inversion algorithm was applied to a CSAMT field data set collected along a profile over a tunnel construction site at Hallandsasen, Sweden. To avoid erroneous inverse models from strong anthropogenic effects on the data, two scalar transfer functions (one scalar impedance and one scalar vertical magnetic transfer function) were selected for inversion. Compared with a regularization of distortion parameters with the Marquardt-Levenberg method; the minimum-solution length criterion, yielded smaller absolute values of distortion parameters and a horizontally more homogeneous distribution of electrical conductivity.