Can't get rid of interlace lines

[MacFast]

Got a new grandchild so I figured it was time to get a video camera. Here's what I got:
1. Cannon Vixia HFM 31. Records HD video in AVCHD format.
2. Adobe Premiere Elements
3. Pinnacle Studio HD Ultimate V15 (theoretically free after a rebate that has yet to arrive).

Here's the problem: I'm having a hard time getting rid of interlace lines when I make a DVD. I've tried recording in both 60i (interlaced?) and PF24 (progressive?) When I use either editing package in its most basic form, the DVD I produce has interlace lines when I put it in my Sony DVD player and watch it on my Sony LCD TV. By "most basic form" I mean that I drag the clips onto the timeline. Trim the scenes. Add transitions, and click "make DVD". Seems like it should work since I'm basically just using the default configurations, but it doesn't.

I've checked the menus on both the DVD player and the TV. There is no option to switch from interlaced to progressive on either. There is a progressive output option on the DVD player, but it only works with the component video output. I use HDMI. I turned it off in any case.

There is one thing that does work. The Pinnacle software has an option to create a DVD (VideoTS) file, and under that is a checkbox for "progressive output". When I do this and burn the resulting file to a DVD the interlace lines are gone and the video is beautiful. However nothing else I've tried works. The Adobe software has a similar option, but it doesn't have the same effect. The interlace lines are still there.

Also, when I view the files on my computer monitor, without burning to DVD, the interlace lines appear there also, except when using the Pinnacle progressive option described above. I figure that's because the monitor is progressive display.

So, anyone have any ideas on what's wrong?

[aedipuss]

the camera records in 30i 30p or 24p. what are you recording video in? most dvd is 30i so "lines" shouldn't be visible if the video is recorded to the default 30i then converted to 30i dvd spec mpeg-2.