Lighting dust, haze, smoke and mist (water vapour/steam technically refer to the gaseous state of water and is thus invisible, like air) is all a matter of contrast.
As Jay states the problem lies with the fact the background is brighter than your subject. Here's an example of the opposite effect where the mist emerging from a chimney at York Minster catches direct sunlight and is seen much brighter than the surrounflding walls (which are in shadow) and even the blue sky!
If you can't engineer it so the the sun strikes your mist and not the background then a good alternative is to use an auxiliary flash.
The angle of the light is not overly important as mist is diffuse and so reflects light equally in all directions (so it will appear the same regardless of the lighting angle). The key is to get the light as close to the mist as possible, light diminishes in intensity with the square of the distance. This means that if your flash is 1 meter from the mist and 10 meters from the background the mist will receive 100 times the light!
It is important to angle the flash so that it doesn't shine down the lens, and not pointing it directly at the background will help contrast a little. You ought to be able to get a decent contrast with the onboard flash even if it is pointing towards the background if you shoot in twilight and use the fastest shutter possible (usually 1/250)