Preheat barbecue to medium-high. Cook potatoes in boiling salted water until tender, but firm, about 14 minutes. Drain and cool slightly.
Toss peppers in 1 teaspoons olive oil. Place on grill, close lid and cook until skins have blistered, turning once, about 8 minutes. Place in a bowl, cover with plastic and let cool. Peel and seed peppers. Cut into bite-sized pieces.
Separately toss onions and potatoes with 1 teaspoons olive oil each. Place onions in a grill basket and cook for 5 minutes. Add potatoes and cook until tender and nicely charred, another 5 minutes; turning as needed.
Add potatoes and onions to peppers along with remaining oil, mayonnaise, balsamic vinegar, salt, pepper and green onions; toss.