Hi Cabe,
What your showing is known as a Rail-Splitter circuit. A more developed version of your circuit would involve an Op Amp to buffer ground. If your circuit doesn't draw to much current (less than say 40mA p-p) then the Texas Instruments TLE2426CDRTLE2426CDR will do an excellent job, if you look through the application notes you'll see how it works, if you need to sink or source more current then adding a dedicated buffer will do the job.
Go to TI.com and search for TLE2426CDRTLE2426CDR APP NOTE SLOS098D
If you google that component you'll get other ideas for creating virtual grounds.
You had the right idea Cabe, and your circuit didn't draw enough current to destabalized the ground reference, so if you want to improve the design the TI part above is the way to go. In college one of my classmates used the above component coupled with an instrumentation amplifier to make a rudimentary EKG machine out of an oscilloscope. The results were suprisingly good.
Hope this helps.
Regards,
Jorge Garcia
HI Cabe,
I actually forgot to include in my previous post, and I think you may have gotten your image from this site, but just in case read through this webpage the information is pretty accurate and I think it will give you a clear understanding of what you can do in the future.
http://tangentsoft.net/elec/vgrounds.html
Hope this helps,
Best Regards,
Jorge Garcia
Cadsoft Computer