Here's a good site for determining when the moon will rise and what phase it's in: http://aa.usno.navy.mil/data/docs/RS_OneDay.php

Looks like full moon is on June 18. A full or close to full moon isn't ideal for observing, as its brightness and orientation to the sun makes seeing much detail a bit difficult. Best time for observing the moon is when it's 1/4 to 1/2 full or thereabouts. Regardless of phase, observing other targets when there's a moon out is problematic as well, as its brightness washes out most other astronomical targets.

All is not lost however, you should still be able to get a good view of Jupiter that night, its bright enough that even a full moon won't affect it too much. You may also be able to make out some of the brighter open and globular clusters.