Joint CD and DVD Burning

Anybody have any idea how I would go about burning a joint CD and DVD? i.e. a disc that would play the audio tracks when in my cd player and play both the audio and video when in my dvd player.

Similar to what is sometimes released in the music industry - cd album r single with bonus DVD.

Is this possible and if so what sort of disc and software would i use?

Then you must use a CD-R or CD-RW, no cd player can read DVD media!

And do I just burn the video onto the cd as avi files?

will these then play on my DVD player?

Better to keep it separated.
What you are looking for is a kind of a CD audio put together with a kind of DVD video (or VCD/SVCD/DivX on a CD).
CD players look for audio CDs that a specific format - if your CD player starts reading other kind of files - and video will be some kind of data files for it - it main ruin your loudspeakers.
Some DVD player can play different kind of files - like jpeg images - after you choose them from a menu, but you will not have video at start (like a DVD) and you would need a player compatible with such a facility - not a normal requirement.
At blank prices - keep it simple, bur a CD and A DVD, keep them in a slim double case and get away from trouble.

This operation you are try to do is unconventional and it is most likely won’t work, For play CD-R you need the CD-ROM and for playing DVD Movie file you need DVD=ROM.

It seems to me that some DVD-Audio discs are double-sided, with the DVD-Audio on one side and CD on the other (I have at least one like this - Rob Thomas’ latest album), but as far as burnable media goes, I’ve never seen any double-sided burnable media other than DVD-RAM (and that is rare in double-sided format)… and certainly not double-sided hybrid media.

This is called [B]DualDisc[/B] and displaced itself from the market due to many incompatiblities and issues!
Such mediatype is not available as writeable disc. Also doublesided recordable media is DVD-R (DVD10).