Beveled edge along profile

I am not sure if this is the correct forum to post this, but I am having trouble creating a feature in a part. I don't have any idea where to begin.

Basically I would like to profile a beveled edge along a curve with another curve being the centerline. It's difficult to explain without a picture, so here's one.

Instead of the face in grey being flat, I'd like it to have a beveled edge that meets in the middle of the curves.

Any ideas on how to model this?

Thanks,

Lee.

SolidworksSurfacing