Well, a house is different from a balcony. I use plastic for the ones that sit on my window sill ... not the prettiest, but all I could find that would just sit on my window sill without support and still be a decent depth.

I also have window boxes sitting on the ground, and for those I use foam that looks sort of like stone. Got them at Home Depot.

I found some stone-like plastic ones at HD that were a good depth, but yeah -- only about 2 ft. wide. You could put two of those next to each other, but for a good-sized box you'll probably want to check at a *real* garden center. Our nearest one is ridiculously pricey, but if your box is a permanent installation, it's probably worth it. Nursery guys and people at more prof. garden centers are usually filled with useful information, too.

Couldn't say about the neighbor's suspended box -- maybe a plate of brownies and a pitcher of lemonade will get you the secret!

Just a thought....but if you're handy then you could get some cedar fence pickets and build your own...

I built a 24" square planter out of 8 pickets, and it only cost me $8 plus 1 hr in the woodshop