Hi minoss
There are several possibilities:
1.) Look for zero-crossing on both channels. Measure the frequency (time from zero-cross to zero-cross multiplied by 2) of one channel. Measure the difference between the zero-crosses (identical edge) of both channels. So you can calculate the phase shift.
2.) Transform the input-signal to a logical signal (only '1' and '0') XOR both channels and do a lowpass-filtering. The output-voltage is proportional to the phase (works only from 0° .. 180°)
Bye