Is it possible to model roads below the surface?

If you define a negative height to a link, the link will be displayed below the 0-plain and thus is not visible in 3D mode initially. However, vehicles will still travel on such a link and you can look below the 0-plain in 3D mode. You can also shift the entire network (excluding background files) to a different height using the z direction in 'Edit - Translate Network'.

From Vissim 6.00 it is also possible using levels