My wife made me a storage solution for Christmas out of stackable ornament boxes with egg-crate foam added to the bottom of each compartment. She also pulled the dividers out, but you could go either way on that. It's pretty freaking awesome, especially because it's easily expandable and cheap. You can also just fill up one compartment with minis you know you'll need and just take that.
If you have the option to go with some kind of model, toys, etc. that allow you to see it, that's best.
If you don't, here's some options:
1) Two layers, two colors
On your map, use two colors of markers - one is the upper level, one is the lower level. For your mini's, you'll want something like colored rubber bands, flags or to stack them on top of a base/token indicating which ones are up top/lower down.
2) Breakout map
This only works if you don't have too much overlapping area - you can put the upper areas parallel and further out on the same grid map to the lower areas. I've used this for a fight on a series of platforms/construction scaffolding, and it worked well enough.
3) Parallel maps
Get several separate map grids, each one representing a different level.
This works best if there's a lot of overlapping areas, where people might run/climb up and down, but not where they'll be fighting, shooting arrows, etc. between floors very often. You want to keep the action on a single map and not have a mini on one map shooting ranged attacks at someone down stairs, which means running over to the other map and seeing how they line up.
All of these require you, and your group have good spacial visualization and communications skills, otherwise you just end up with people MORE confused. Usually terrain made even of cardboard or legos, works best for visualization and for more people keeping track of their positioning.
Best Answer
I just ordered some minis off rpglocker.com (Not affiliated with them in any way.)
Most of the stuff here is from Wizards, but you can buy them individually so you don't have to get an entire set for one character you want... The prices seem reasonable (about $1 per for most of them) and there was a pretty large selection.
Also, the guy was really easy to work with and kept me up to date on the status of the order. They're supposed to be here Friday, so I'd be more than happy to update you with the satisfaction of them then. I'm optimistic.