The two-photon interband electron transitions in a silicon layer directly underneath the Si(111)-SiO2 interface in the vicinity of the E-2 critical point (CP) are probed by optical second-harmonic (SH) spectroscopy. The combination of the SH phase and intensity spectroscopy allows the complete deconvolution of the spectral behavior of the amplitude and phase of the quadratic susceptibility chi((2)) near the E-2 critical point of silicon.