We do use the CMB as a frame of reference, since we are now able to measure the wavelengths quite accurately in every direction:

http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation

CMBR dipole anisotropy

From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 627±22 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB) in the direction of galactic longitude l = 276±3°, b = 30±3°. This motion results in an anisotropy of the data (CMB appearing slightly warmer in the direction of movement than in the opposite direction). The standard interpretation of this temperature variation is a simple velocity red shift and blue shift due to motion relative to the CMB, but alternative cosmological models can explain some fraction of the observed dipole temperature distribution in the CMB.

What's being measured is not the speed of light which, as you say, is the same for all observers, but the temperature/wavelength/energy of the light (EMR if you prefer) which is subject to Doppler shift.

"Time is what prevents everything from happening at once" - John Wheeler