The light from the two stars would be Doppler shifted in a sinusoidal pattern (for a circular orbit). The signals from the two stars would be in anti-phase and would oscillate at the orbital period of the binary.
The planet would cause a small pull on the binary system which would superimpose a further small sinusoidal signal (again, assuming a circular orbit), but at the longer orbital period of the planet around the binary system.
The process is illustrated below by adding two (red and blue) sine waves together, where the blue sine wave has a much smaller amplitude and lower frequency than the red sine wave. These sine waves encode the Doppler shift that would be measured from the absorption lines of one of the binary components. Thus the red wave would indicate the Doppler shift due to the motion of the binary system and the blue sine wave the additional modulation due to the smaller motion induced by the tug of the planet as it orbits. The black line then gives the superposition of these (they can basically be added if the velocities are non-relativistic) and you can see that it is subtly different from a monochromatic sine wave of fixed amplitude.
For non-circular orbits, the pattern of Doppler shifts would be non-sinusoidal but still periodic in a similar way.