Hello Scotch Lad,
Well spotted, yes a full bottle of LPG propane or butane does contain both liquid and vapour phases, though I think you knew that already.
For anyone else who is interested, here is my 'Blue Peter' explanation of how LPG bottles work.
Both propane and butane have the characteristic that if you compress the gas enough it will change phase into its liquid state. This will also happen if you chill the gas, which is why at about 0 centigrade, butane converts to liquid and stops providing gas to the caravan. The same happens for propane but the temperature is about -40 Centigrade (it also happens to be -40 Fahrenheit as well its just where the temperature scales cross).
The bottles work in exactly the same way as a pressure cooker. When no gas is being consumed, (and assuming the bottle is warm enough) the liquid boils (yes boils!) and produces vapour. The pressure inside the bottle rises until it matches the vapour pressure for the gas, when it suppresses the boiling.
When you take vapour or liquid off the bottle, the pressure drops so the liquid starts to boil and releases more vapour, until the pressure is restored to prevent further boiling.
In a domestic pressure cooker, you need to apply external heat to the cooker to maintain the pressure, In the LPG bottles exactly the same external heat is needed, but in this case it collects the energy from the temperature of the air around the bottle. - This also means that the bottle tends to self-cool when gas is being used. This has implications for butane in winter, where the air temperature may be above freezing, but because of the energy used to vaporise the LPG, the bottle temperature will fall and may prevent vaporisation thus no gas in the caravan. A typical demonstration of this effect is when roofers are boiling their bitumen using a propane bottle. With the burner on, the bottle cools and forms frost around the liquid content of the bottle.
The same effect is used by some bottle content indicators, that use temperature sensitive liquid crystals that change colour according to the surface on which they are attached.
As for the pressure inside the bottles, as both liquid and vapour are coincident in the same sealed volume they must assume the same pressure (ignoring hydrostatic heads due to the height of the bottle).
The actual pressure is dependant on the type of lpg, and the temperature of the bottle. Propane has a greater vapour pressure than Butane.
Sadly in this commercial world none of the gas is free!