This is classic, the effect is called Mie scattering.
Very simply speaking, light is scattered on the whole surface of every (translucent) particle. For round particles, interference makes a diffraction pattern with conic symmetry, i.e. the intensity of diffracted light depends on the angle towards the incoming wave.
Obviously the pattern depends on the light wavelength, and so there is a dispersive effect. It's not very strong, because usually the particles are not all exactly of uniform size, and there is a lot of multiscattering.
Btw. it takes a keen observer to notice this without prior knowledge. Congratulations. ;-) It's easier to see if you dilute the milk (less multiple scattering). At least one good use for low-fat milk.
Warning: The explanation above is terribly simplified, to the point where it doesn't explain much. For example you'd expect the colours to change with every brand of non-/homogenised milk, because the size distribution varies. Not so much.
Also the effect is obscured by the fact that light scattering is generally much stronger for shorter wavelenghts. That also means that red light is more likely to pass through, and blue light to get absorbed or escape on the front side. It's really hard to tell apart Mie scattering and the ordinary Tyndall effect.