Joint migration inversion (JMI) is a recently proposed full wavefield inversion method, which tries to minimize the mismatch between observed reflection data and forward modeled data, which is based on decoupled velocity and reflectivity models. Transmission effects and surface/internal multiples are included in the forward modeling process using a multidimensional version of the Bremmer series. However, since the current implementation of JMI uses an angle-independent reflectivity model, it cannot easily handle large-offset data due to the amplitude versus ray-parameter (AVP) effect. In this paper, we propose to use a zero-lag cross-correlation objective function of redatumed wavefields to mitigate this AVP challenge in JMI. This objective function can help to relax the requirement for strong amplitude matching happening in the least-squares sense and focus more on the similarity between the modeled and the measured data during inversion. For the reflectivity update, by weighting the corresponding redatumed residual wavefield, the correct value of reflectivities is mostly preserved. For the velocity update, we weight the redatumed residual to minimize the amplitude influence and emphasize only phase information. We demonstrate the effectiveness of our new method with a velocity model containing a strongly scattering overburden and a 2D realistic deep water model.