Should you wish more details, the regimental histories of the several Hessian units give considerable detail on the structure and strength of the units at this time. Unfortunately, they are not available for sight on Google to those in Europe. I include this information as I found these on a trip to the United States and reviewed them with respect to the later period (siege of Graudenz).
Geschichte des 1. Grossherzoglich hessischen Infanterie- (Liebgarde-) Regiment by Carl Christian Röder von Diersburg (Freiherr.) - 1899
from page 111 on the Leib-Brigade.
Geschichte des infanterie-regiments Kaiser Wilhelm: (2. Grossherzoglich Hessisches), Issue 116 by Wilhelm Bigge - 1903
focus is on the fusilier battalions from page 70 (with a color plate between pages 70 & 71).
Geschichte des Infanterie-Leibregiments Grossherzogin (3. Grossherzogl. hessisches) Nr. 117 und seiner Stämme 1677-1902 by August Justus Alexander Keim - 1903
covers Brigade Landgraf on pages 166-167. There is a short discussion of the regulations on pages 169-170.
Geschichte des 4. Grossherzoglich-Hessischen Infanterie-Regiments Prinz Karl Nr.118 und seiner Stämme 1699-1878 by August Keim - 1879
covers the Brigade Erbprinz on pages 105-106
The structure established in 1803 was modified in 1806 with new names (for example the Leib-Brigade became the Leib-Garde Regiment and the two battalions of the Landgraf Brigade became the Leib-Regiment).
For completeness, the cavalry are covered in:
Kurze Darstellung der Geschichte des 1. Großherzoglich Hessischen Dragoner-Regiments (Garde-Dragoner-Regiments) Nr. 23 von 1790 bis zur Gegenwart by Karl von Zimmermann - 1894
I recall seeing something on the artillery, though I can not locate it at the moment,. - R