Minecraft – Are there underground mobs in peaceful difficulty

As of 1.8, setting difficulty=0 is the new equivalent to peaceful. spawn-monsters=false will still get rid of the nightly mobs, but unless difficulty=0, spawners will still spawn, and your health and food will not regenerate.

BEGIN OLD ANSWER:

In order for the changed setting to take effect, the server must be restarted. until restarted, monsters will still spawn. After a restart, there should be no monsters.

There are two points to remember that may seem contradictory: first, like Nicholas pointed out, you need to makes sure that your mobspawner is the only nonlit space in a pretty big area around you (I think the area's actually about 150x150 blocks), but second, you need a lot of empty space around. In other words, minecraft will choose places that have a lot of surface area (not volume) to spawn mobs in, so if you were to have a lot of open caves beneath your mobspawner, the game will flag that area as more likely to spawn mobs in. You just also have to make sure that it's all well-lit, then you've effectively tricked the game into flagging that area to spawn mobs in, but then conveniently your mobspawner is the only dark area where it can do so.

I would recommend you take a look at this tutorial. You may not want that particular style of mobspawner, but it goes over the prerequisites of any good mobspawner quite nicely.