The generalized phase contrast (GPC) method is explored for improving the accuracy in quantitative reconstruction of two-dimensional phase distribution from images of semi-transparent objects viewed with a common-path interferometer (CPI). We propose a novel optical scheme for highly accurate determination of the object-dependent complex synthetic reference wave (SRW) in a CPI. Using a simple 4f imaging optical setup, GPC provides an analytic model of the SRW profile that is shown here to increase phase measurement accuracy over the entire output aperture. The improved accuracy due to the GPC model can exceed one order of magnitude compared to that of the conventional plane wave model of the reference beam. Furthermore, we describe a novel method for accurate derivation of the strength of the phase object's zero spatial frequency component based on the intensity of the traditionally ignored halo region encompassing the interferogram. Combining this information with three inteferometric measurements, full-field phase images with unconstrained phase strokes are obtained accurately.