We investigate the nonlinear propagation of intense, two-cycle, carrier-envelope phase (CEP) stable laser pulses at 1.7  μm center wavelength in air. We observe CEP-dependent spectral interference in the visible part of the forward-propagating white light generated on propagation. The effect is robust against large fluctuations of the input pulse energy. This robustness is enabled by rigid clamping of both the peak optical field and the phase of the propagating waveform, which has been revealed by numerical simulations. The CEP locking can enhance the yield of the CEP-dependent strong-field processes in gaseous media with long-wavelength drivers, while the observed spectral interference enables single-shot, stand-off CEP metrology in the atmosphere.