Arduino Nano 3.0 dimensions without the pins
Mini-USB-B is around 4mm tall. 

Most PCBs are around 1.6mm. 

The FT232RL on the bottom is 2mm (max) according to the datasheet. (voltage regulator is 1.8mm). (I'm sure about this tantalum capacitors)

So that's something around 7.6mm total height