Carrier-envelope phase (CEP) drift of a pulse train of 2 ps pulses has been measured by a multiple beam interferometer. The round trip time of the interferometer is slightly mistuned from the pulse sequence, leading to spectral interference fringes. We extract the pulse-to-pulse CEP drift from the position of the spectral interference pattern. The length of the interferometer has been actively stabilized to ±10 nm, which sets the ultimate limit on the accuracy of the measurement to 78 mrad, while the CEP-drift (rms) noise of the measurement was 127 mrad (at 800 nm).