I have some Hirtenberger .308 that has a steel case around a lead core, with a copper "wrap" for lack of a better term, around the steel. I did a Saeco hardness test on the steel and it is pretty soft. Can't recall the number though.
The copper jacket over the steel is relatively thick. I recovered some of the projectiles and the rifling marks look to be the same as a standard copper jacketed bullet. These don't group worth beans, but they make noise... and the brass is good.