No, 1080i means it's 1080x1920 but each frame only has info from half the vertical (1080/2=540) lines. Okay, that's not technically true but it's a simple way to think about it. 720p means you have complete 720x1280 frames every frame.
I believe you mean 1920x1080 (Full HD), and 1280x720, but you do have your facts right about 1080i being interpolated. ;-) You'd have some strange resolution (tall) using the numbers in the order you gave.