Rain being a douche

[The chaser]

Another way of having both fog and rain is: Turn the alpha channel of the fog down to around 0.6/0.7. And instead of using planes in a box arrangement around the fog, set the skybox active and make it (exactly) the same colour as your fog box. Also, set the alpha channel of your rain particle system higher than 1 (just type in 2 or 3, adjust it accordingly until looks better :-) ). Hope that works! The chaser's method also works, pretty sure I used a combination of both for a mod I did a while ago.

Fog cannot be seen when there is nothing it can cast on. Fog cannot cast on a skybox.

With a 0.7 alpha, it will be slightly transparent and you'll be able to see everything (if it has transparency, you can see stuff, regardless of the Start/End of the fog. What sonataarctica said is to do that and then making the skybox as same as the Fog, so there's the ilusion that there's always fog when the skybox fakes it.