I know the Edict of Milan was for Christianity, but did the Jews (also being monotheistic) gain some rights as well? What was life like for Jews before and after the edict?
The Edict of Milan by-and-large did not affect Roman Jews. Jews already had a special legal status in Roman law. They were allowed to have their own legal system to an extent, and were allowed to practice religion freely. They were excused from participating in the Roman polytheistic religious system, which was unusual--many religions were happy to practice syncreticism, but with Judaism's beliefs this was impossible. The Romans understood and accepted this.
If anything, the Edict of Milan brought Christians on equal footing with Jews. Like Jews they were now permitted to practice their religion freely, organize themselves, and be exempted from Roman religious practice.