I don't know how you can stand looking at an interlaced video display. The flickering would drive me nuts.
By the way, just because the TV can do it, does not make it the native resolution. Again, many 1080i TV's do not run that mode natively. They are normally 720P TV's that can run 1080i, but they do so badly.
One other thing. Are you certain the TV's HDMI/DVI port is compatible with a computer video card output? The DVI port of a computer is slightly different than the DVI port on a TV meant to be used for video from a cable box.