Amplified microphone signal output to ADC input. How can I eliminate DC offset?
Assuming you cannot measure negative voltages, your schematic is good. You have to compensate in your software for the DC offset.

Compensating is as simple as subtracting the offset; you could implement a calibration procedure, or use a long-term average of the input values to correct for this offset. The latter has the advantage of being fully automatic and compensates for drift.