Calculating common length of two lines using ArcGIS Desktop

I have a shapefile that consists of around 800 different lines.
Now I have another shapefile which also consists line data.

Is there a method which can help me calculate the shared length in the second shapefile with the first one?

The lines of both feature classes are not necessarily overlapping.
For example both the lines are crossing through the same road but on different corners. As seen in the picture I want to calculate the length, separately of the black line where it passes near the red line and also where it does not.
For one or two lines I used the split tool and calculated the length manually but I want to do it for all the lines.