Yes they're all fully detailed with working hatches and an office on each floor etc. These boards should be making an appearance at the Mantic Open Day at the end of the month, so when I've got it all out again I'll take photo's of the interiors.
We didn't really use the interiors on these games as it can make it awkward when teaching someone the rules. When we do use them then yes, we leave the floors above the figure off so you don't forget where they are. When fighting up and down a warehouse, we usually leave the ground floor on the board and lie out the upper floors next to each other on the board edge so you can just play through.