Unless I'm missing something, OP is not asking about converting 720p to 1080p. He references "SD" from a DVD, which is not 720p but something (non-HD) less than that.
Some have said that it can't be done and others have said that it can so I'll try to give a "both" answer: it can be done, but the quality of the SD cut insertions will disappoint intermixed with the 1080p cuts. You see this often in documentaries and sports on HD channels where one switches from current (HD) video to showing something shot in pre-HD days. For instance, watch any sports documentary on ESPN or similar where they have players & coaches in the present (shot at HD quality) reflecting on some old team from before about 1999. If they slug in some video shot back then, the old ESPN HD bars are likely to pop up on the sides (because a lot of SD is not shot widescreen) and you'll probably see the lines of the old video because they are fitting about 525 lines of SD into the 1080p lines of HD. It's not quite as dramatic as color vs. old black & white footage intermixed but it's pretty glaring (hopping back & forth between say a modern Bball game on ESPN HD to an old game on EPSN Classic on the same "full HD" television might be a quick way to grasp this point). Since OP sounds like he's working with a DVD movie, he might not have a widescreen problem but there's no getting around having only 525 (or less lines) trying to fit into a 1080 lines of full HD (via that Blu Ray).
phrehdd, I think you might be thinking of DVDs claims to (I think) 704 or so pixels. I think they are something like 704 X 525i lines vs. 720p which is 1280 pixels by 720 lines. If OPs "SD" version is as you think- 720p- it will be much easier and more effective to upscale 1280 x 720p to 1920 x 1080p instead of approx. 704 x 525i to 1920 x 1080p. The 720p to 1080p is not even close to having to make up so many pixels to fill in the gaps (and yet, it is still about a million pixels to be invented even there).
Scalers- especially professional equipment- can work wonders but you're still likely to notice
especially if you are cutting & intermixing HD & SD such that it is flipping back & forth (again ESPN HD vs. ESPN Classic example). The eyes will notice a shift from relatively crisp to blurred and/or with SD scan lines showing, etc.