Is that possible to get a complete music release for MIB 3 like MIB 2 ?

Probably not, it is still in theaters. The only ways are a) if a composer's promo leaks, as with MIB 2, or b) someone does a dvd rip, but that can't happen yet.

Is there anything new yet?

Yeh also interested in this, mainly the film version of "the mission begins"

I think I would be more interested in a complete score for the first MIB...

This score, unfortunately, was nothing "Ear Popping", but I did really enjoy the end of "Mission Accomplished", where *SPOILER* Agent J finds out it was actually his father that gets killed and young Agent K takes care of the little boy, which he realizes is himself. Beautiful scene.

Spoiler Alert:

And I liked that score. I'm hoping Danny releases more.

If anyone finds anything new, please let me know.