^Very close but not quite right.
DVD-video has a maximum resolution of 720 x 576 in PAL systems or 720 x 480 for NTSC, but it is possible to burn high definition avi, mp4 or mkv files on a recordable dvd. Your Sony home theater probably won't be able to play them, but you can play such files on a home computer with no problems. So while it is possible, it is not a solution for your particular situation.
There are new media players out that can handle high definition in other formats than AVCHD or Blu ray. Look at something like the Western Digital HD Media Player: http://www.bhphotovideo.com/c/product/696925-REG/Western_Digital_WDBABX0000NBK_NESN_WD_TV_Live_Plus.html This player has no optical drive, but can use video on usb storage devices. These players are growing in number and capabilities, but are bypassing optical storage for the most part in favor of usb drives, internet streaming and hard drives.