Baked lights with realtime directional causes black shadows

I'm trying to get to grips with Unity's lighting features. Ideally, I'd like to have point lights in a scene which are baked, but have the directional light be realtime, so I can still have realtime shadows in the scene. When I do this, any area with a realtime shadow becomes completely black.

I set up a test scene to try out various mixtures of lights. In the scene, the floor and the left cube are static, and the right cube is not static. The red point light is set to baked, the directional light is grey and realtime. The ambient colour is black and reflection is turned off.

You can see the mapping from the red light is correct, but the shadow from the directional light is completely black, even in areas where the red light should be illuminating it.

I would hope that it would look something like this, in which I lowered the shadow strength.

Am I missing something obvious here? I don't feel like there's a lot of room for misinterpretation, so is a realtime directional light just not compatible with baked point lights?

Thanks in advance for any help or pointers!