We present a novel phase generated carrier (PGC) demodulation technique for homodyne interferometers which is robust to modulation depth variations and source intensity fluctuations. By digitally mixing the waveform with a multitone synthetic function (a linear combination of harmonics of the modulating signal), distortion can become negligible even in presence of large variations of the modulation depth. The technique only requires two mixers and can also provide the DC component of the phase in real time, without needing any previously recorded data or ellipse-fitting algorithms. We validate the technique with simulated waveforms and with experimental data from a wavelength metering experiment using an integrated unbalanced interferometer on-chip, showing that the technique corrects distortion without increasing the noise with respect to the standard PGC technique.