Stir together first 8 ingredients in a large bowl. Gradually whisk in olive oil in a slow, steady stream until blended.
Alternately thread monkfish, eggplant, and mushrooms onto 8 (8-inch) skewers; brush with sauce. Cover and chill 30 minutes.
Grill, covered with lid, over medium-high heat (350° to 400°) 5 to 6 minutes on each side or until done.