My head is hurting here, guys. Can someone help?

Ive recently got an LCD HD TV. Im watching NTSC DVDs on it upscaled to 720p. My TV says it is running at 60hz refresh rate.

But this confuses me. Doesnt standard DVD already run at a rate of 60hz when playing interlaced footage?

Each video frame is broken into odd fields and even fields. If so, doesnt progressive scan show both fields at once, thus making a refresh rate of 30hz - odd and even lines merged together per frame, as opposed to showing both sequentially? Or, does it show odd and even lines together twice, like this?

[ ]denotes a single frame of video

INTERLACED: [OE], [OE], [OE], [OE]....
PROGRESSIVE: [OEOE], [OEOE], [OEOE], [OEOE]

In other words, the split second used for showing odd lines in interlaced video is now used to show both fields at once, and this is repeated for the split second that would be used for showing the even lines? Is that how it works?

Ive gotten so confused trying to work it all out that I can't think straight anymore