Place steak in a shallow dish or large heavy-duty resealable plastic bag. Combine water, soy sauce, Worcestershire sauce, onion, vinegar, juice, mustard, garlic, parsley, thyme, Italian seasoning and pepper; pour over the meat. Cover or seal and refrigerate overnight. Remove meat; discard marinade.
Grill, uncovered, over medium heat until meat is cooked as desired, about 6-7 minutes per side for rare, 8-10 minutes per side for medium, or 11-13 minutes for well-done.