The basic solution is to AC couple the headphone output to the high impedance analog line level input of the next stage/device. The next stage should be a self biased input in this case. The AC coupling capacitor value should be calculated based on the ground referenced impedance of the next stage, as it will form a high pass filter with it.
Be sure the parasitic capacitance, connected directly to ground rather than in series with a high impedance, is minimized as the headphone output can only drive about 100pF of ground referenced capacitance. The negative side of active outputs can have a large coupling cap in single ended operation.
This solution should work either for differential or single ended designs. As far as register settings, we recommend the differential or single ended modes (MODE 000, 001, 100, or 101) as best fits your application. The capacitor-less modes (010 and 011) and fast turn on modes (110 and 111) are not ideally suited to this application.