Combine marinade ingredients in bowl.
Pour marinade into resealable plastic bag.
Add artichokes and mushrooms.
Seal bag securely.
Turn bag several times so marinade coats all the vegetables.
Refrigerate and marinate for 2 hours.
Drain and discard marinade.
Thread artichokes and mushrooms alternately onto skewers.
Preheat stovetop grill.
Grill vegetable kabobs over medium heat for 3 to 4 minutes, turning every minute or as necessary.
Cook until vegetables are tender, or to taste.
Vegetables should begin to brown on the outside and be tender on the inside.
Remove kabobs from grill, set decoratively on platter, and serve on a buffet or pass at the table.