Light outside, but dark inside a cave

So I have a problem I’m not sure how to solve at all in Unity 4.5. I have tried some different ways, but I’m hoping someone else has got the same problem and can help me how to solve this.

I want to have a day and night cycle, and I use directional lights for this as they light the whole world. I have gotten that the cycle to work without problems. However, the problem I’m having is that they also lights up inside my houses and caves (even without having the windows). This make a problem since I cannot make it pitch black inside any where, even where there is no lights at all. Does anyone know how to solve this?

I assume other games have had the same problems so I’m really curious on how you solved them, or if there is just no way to solve it.

Enabling shadows on your light, and making sure the cave’s parts have “cast shadows” and “receive shadows” enabled should do the trick. Also, try tweaking the ambient light level down a bit in the render settings.