Having provided the Hesse-Darmstadt unit histories (which can not be viewed in Europe), perhaps the following for Hesse-Casel might be of interest:
Kur-Hessischer Staats- und Adress-Kalender - 1803
The structure of the military starts on page XVII (one can type in "xvii" to get the page or, if downloaded, it would be view 53) and the regiments start on page XIX.
Another work covers a broader sweep of time:
Stamm- und Rang-Liste des Kurfürstlich Hessischen Armee-Corps vom 16ten Jahrhundert bis 1866 - 1866
The 1803 period gets only a few lines on page 57 and 58, although it sits within a context.
The presentation by individual unit include a short service summary (the first individual unit starts at page 115).