Wow.....I'd be surprised if any orthopod, much less the prosthesis manufacturer, would recommend that you do any running with a total hip. There's a much greater risk of stem fracture and prosthesis loosening with impact activities. At the very least, you'd be accelerating the surface wear on the prosthetic components. Hip revisions are more difficult, less bone stock to work with, blah, blah blah (all the stuff your orthopod has likely already told you).
Saying all of this, running on a treadmill is likely less compressive than running on roads (at least, it is in total knees). If you're determined to run, stick to the mill - I wouldn't run on the roads at all.