Helium is the obvious candidate, it's only slightly heavier than hydrogen. It's not flammable or explosive, and it works well in balloons.
There are three fundamental problems though which makes the idea unrealistic:
Where does it come from
Where would all that helium come from? The chemical makeup of the planet would be very different from our own.
Why does it stay separate
You would expect atmospheric mixing to constantly churn the atmosphere. Oxygen, Nitrogen and Carbon Dioxide all have very different densities but they still mix fairly evenly in our atmosphere.
Why doesn't it escape into space
Lighter gasses escape more easily, you would expect Hydrogen and Helium (especially in the upper atmosphere) to be stripped away into space by atmospheric escape.
A possible solution
There is one scenario that might just work although it's still rather implausible. That is if the planet was a moon in low orbit around a gas giant. The gas giant would be the source of the helium and hydrogen, replenishing that which was lost and causing escaped gas to remain in a ring to be gathered in again as the moon orbits.
That doesn't solve the atmospheric mixing problem but you can hand-wave that to a certain extent.