Phase shifting DC+AC audio signal without affecting its DC content
to obtain the exact DC bias level of this composite signal


Use a low pass filter - it will average the signal and give you the DC level. Of course, you will need to take into account that a low pass filter will take time to settle to the average value and that there will still be some rippley artefacts left from the AC content of your signal but by choosing the correct number of stages you will get a small ripple that will likely be acceptable to use.

Following a discussion it appears that the op wants the dc level representative of the on-off periods being equal so: -



The comparator turns the analogue signal into a square wave. If the duty cycle isn't 50:50, the integrator raises or lowers the comparator threshold until it is. Bingo, there's the output.