Yes, it is possible to capture sprites and jets with a DSLR, however you need to use very short exposure times to reduce any background glare. With moonlight I had to go down to 1 second. It is much better to use a modified DSLR (no IR-blocking). How to know when to stop clicking and check the many files... this is where CCTV video-based detection (or night-vision equipment) comes handy. It is possible to see the sprite with your eyes but it is more likely to miss it. I only start taking photos as soon as the system has started to produce sprites at a somewhat steady rate (usually once per 1-5 minutes).
For jets you need to be very lucky. Be close to the storm, preferably within 50 miles, because blue light is scattered a factor of 5-15 more than red light with distance. There have only been few observations of jets since their discovery in 1994. Some amazing jets were recorded last fall in Japan from a supercell having incredible flash rates. Typically one could expect a jet once in a few years of continuous observation. The same for trolls, which is a freaky interaction of sprites and the storm resulting in a bunch of upward things looking like jets or gigantic jets. We got a new one over southern France last September.
If you want to get seriously involved and sure to get images, take a CCTV setup (Watec 902H2 Ultimate, 8, 12 or 16mm lens, video grabber, computer with UFOCapture). A color camera like Watec 221S would also work, albeit slightly less sensitive. Use also a GPS time inserter, you and the scientific world will be grateful for it once you capture a rare event. You may want to contact Walter Lyons to join his network. With the same camera setup and wide lens you can do meteor/fireball patrols. With moderate gain settings you can record 6th magnitude stars. For sprites I use only low gain settings.
In any case, it's fun, especially if you like to be awake during the night more than the day! (unless you leave the camera running continuously)
I will update my sprites section soon, I got much better images last year.
Take my Christmas/New Year's greeting card as teaser (despite compression)
http://www.lightningwizard.com/Movies/Video/oscar_wishes2009.wmv
We have now also obtained high-speed videos here in Spain, that's where the real fireworks shows start... but it doesn't seem affordable for amateurs any time soon
Oscar