Why don't we build an interferometer between Earth and the Moon?
Put simply: controlling the phasing would be impossible (not just difficult).  Not only do you have to deal with a constantly changing physical distance but also with the dynamics of the atmosphere.  It's difficult enough to maintain transverse phasing across an earth-based receiver (think adaptive optics);  I can't imagine a reliable way to track the radial variation.  Without that, unless you are sticking with multi-meter wavelength radio systems, you cannot hope to phase up the receivers.