I can understand your confusion, i've been there :)
Lets start with the fact that PulseAudio, like JACK are sound servers in a sense, with different aims in mind though. JACK is aimed at the professional audio user/musician, while PA aims at providing ease of use.
The audio route is a little different than what you have in your question.
all-applications->PA to jack sink->jack audio server -> libasound and ALSA.
This way the PA which is, as usual the default audio output (sink) pipes the sound to jack. The above looks like this in jack's patchbay (after the sink and source modules have been loaded with
the 'system' entries are provided by the ALSA backend, while the PA JACK sink and source are provided by the PA to jack modules.
If you are running some flavour of ubuntu, then you can add the following in qjackctl -> setup -> "options" tab -> execute after startup
pactl load-module module-jack-sink channels=2; pactl load-module module-jack-source channels=2; pactl set-default-sink jack_out; pactl set-default-source jack_in
The above should load the "PA to jack" modules (2 channels L+R for each), and set the default playback device for all applications to be the PA to jack sink module. Additionally it connect the line in/mic input to the PA to jack source input, so that applications that need access to the default input device (such as skype) can get it through the PA to jack source module.
Now if an application outputs sound to ALSA it should playback through the default device , i.e. through pulseaudio. Which begs the question, do you really need jack altogether? And which application is that?
In any case, if the application is jack-aware it should show up on qjackctl's patchbay and then you can connect it in the audio path as you see fit.
For more information see here. Also JACK's FAQ and wiki are tremendously helpful.