Further to previous answers, a word of warning - it is just possible that two of the three skirmisher companies were NOT armed with rifles, as is commonly supposed. The 12 companies of the Brunswick Oels Jager Battalion formed for service in the Peninsula were based on the survivors of the original Black Horde formed by the Duke in 1809 to fight alongside the Austro-Hungarians. The force then entered British pay, and at that time included only one scharfschutzen (sharpshooter) company armed with rifles. According to my sources in Germany, nobody appears to have found any record of the other two companies being re-armed with rifles. The confusion appears to have arisen from the assumption by many British authors that "jager/jaeger" is synonymous with rifleman, which it is NOT in German forces at this time. Jaeger is simply a generic term for light infantryman, which applied to all 12 companies; the remainder of the battalion was musket-armed.
The main body of the battalion served initially with the 4th Division, then as part of the 7th Division; do not buy into the reputation they have been lumbered with as a result of falling foul of "Black Bob" Craufurd. Their combat record was relatively impressive - certainly more so than many of the other "foreign" units of Wellington's army, and possibly almost on a par with that of the KGL, alongside whom they served briefly.
https://www.napoleon-series.org/military-info/organization/Britain/Infantry/WellingtonsRegiments/c_BrunswickOels.htmlThe main body occasionally dropped from 9 to 8 companies; there is no clear indication as to why, but there is some suggestion that one of these companies was considered "grenadiers" and it may have been that its role was considered redundant within a "light" battalion.
The 1809 force included a regiment of hussars and a squadron of uhlans; the latter (who may simply have been a detached squadron from an Austrian regiment - there is some debate) did not pass into British service, but the hussars did and, as JF says, served in eastern Spain and the Mediterraenean. Note that it is NOT the same unit that fought at Waterloo - the 100 Days unit (which is often referred to as the 2nd Hussars) was formed specifically for that campaign from new recruits, whilst the original hussars remained in British service until July 1815. (The surviving rank-and-file of the BOJ Bn was returned to Brunswick at the end of 1814 and became the Battalion Proestler, later the Leib Battalion and fought at Waterloo; it's not clear how many of the officers returned, as many were originally Prussian and may have either retired on British half-pay, or rejoined the Prussian Army.)
If you have any further questions, do not hesitate to ask.