Jenkins - Docker integration
There's a second blog post which goes into more detail about the setup. The missing piece was dockerize which makes the Jenkins & Docker integration painless. If you look into the Ruby app example, there's a Vagrantfile which will set everything up for you, use that as the starting point for your own setup.
Wouldn't you just create a shell script to setup the docker environment as you normally would (or better still push the docker container in to a private repo) and get Jenkins to pull it down and run the test suite inside docker using the daemonised mode?
Maybe you could use directory shares to drop the output of the test data so that Jenkins can read it and display?
Hopefully a point in the right direction...