Ancestry.com just recently uploaded a massive amount of military records for all wars. In researching this area I found 2 John H. Baden's that may apply:

J. H. Baden
Confederate
Maryland
1 Maryland Cavalry
1st Regiment, Maryland Cavalry
Rank In: Private
Rank Out: Private
Film #: M379 roll 1

His date of birth was 1839 and his date of death was 1904. Nothing on the records indicate a date of birth.

******
The prisoner of war record is as follows:
John H. Baden
Confederate
M578_91

******

Ancestry.com military records are FREE for viewing until June 6th, afterwards there will be a fee charged to view the records.