When using multi-frequency techniques for continuum work (i.e. specifying options=mfs to invert), the model will generally consist of a single plane (if derived from clean or maxen) or an intensity plane and flux scaled derivative plane (mfclean). In these cases, the self-calibration tasks can generate the model for all needed frequencies. However, you must tell the self-calibration tasks that the model is a multi-frequency one by specifying options=mfs.
In the case of the models produced by clean and maxen for multi-frequency images, as these deconvolution tasks do not determine the derivative plane, the self-calibration tasks assume that the spectral index is 0.
The line parameter can still be used when performing multi-frequency self-calibration. In this case, it selects out those channels in the visibility dataset that are appropriate to the model. Indeed, the default line parameter can be rather inadequate, and you should give the parameter explicitly.