If your disc is full 1080p, it's a Blu-ray Disc, not a DVD

If you're playing a BD and the player is outputting 1080i, here's what's happening:
1. The player is reading 1080p/23.976fps (or very rarely, /24p) content from the disc.
2. Using 3:2 pulldown (by duplicating fields), it outputs this to the TV as an Interlaced signal.
3. Better TVs will recognise the 3:2 cadence and compensate for it, so what you see after a few seconds detection time is the same as what you would if you had a 1080p setup.
Many TVs however will just treat 1080i 3:2 content as Video, so you will lose vertical resolution and see small jaggies if you look closely enough. What TV do you have?