Circular phase-dichroism (CPD) has been suggested for the characterization of chiral metasurfaces in supplementing the conventional circular dichroism (CD). Conventional CD probes the bulk properties while the CPD, reported recently in 2D chiral metasurfaces using an air-gap Fabry-Perot setup, is based on the surface properties. Here we propose and demonstrate a robust birefringent interference approach to obtain the CPD by replacing the air-gap with a uniaxial birefringent material in which interference is realized by the difference in the refractive indexes for the ordinary and extraordinary components of the material. We measure the transmission phases of metasurfaces fabricated on birefringent sapphire substrates and obtain clear CPDs for chiral metasurfaces but vanishing for achiral metasurfaces. Importantly, our approach can be applied to metasurfaces fabricated on nonbirefringent substrates by add-on birefringent materials. We confirm our results by a Jones matrix method using data obtained from full-wave simulations, and good agreements with experiments are obtained.