We demonstrate a scheme for parametric amplification that allows us to measure the drift of the carrier-envelope phase of the output signal pulses. The method is based on the unique double phase-matching properties of a noncollinearly pumped BBO crystal, making possible the detection of the interference between the signal and the frequency-doubled idler. Additionally, the suggested device greatly simplifies the single-shot measurement of the phase evolution in Ti:sapphire laser amplifiers by dispensing with harmonic synthesis from the spectral edges of an octave-wide supercontinuum.