  We theoretically investigate the role of complex dipole phase in the
attosecond probing of charge migration. The iodobromoacetylene ion (ICCBr$^+$)
is considered as an example, in which one can probe charge migration by
accessing both the iodine and bromine ends of the molecule with different
spectral windows of an extreme-ultraviolet (XUV) pulse. The analytical
expression for transient absorption shows that the site-specific information of
charge migration is encoded in the complex phase of cross dipole products for
XUV transitions between the I-$4d$ and Br-$3d$ spectral windows. Ab-initio
quantum chemistry calculations on ICCBr$^+$ reveal that there is a constant
$\pi$ phase difference between the I-$4d$ and Br-$3d$ transient-absorption
spectral windows, irrespective of the fine-structure energy splittings.
Transient absorption spectra are simulated with a multistate model including
the complex dipole phase, and the results correctly reconstruct the
charge-migration dynamics via the quantum beats in the two element spectral
windows, exhibiting out-of-phase oscillations.
