"It's a good idea to use beard shampoo on your hair, but not a good idea to use hair shampoo on your beard." - Check.
Beardsley is a company that offers specific beard shampoo. The company claims that Beardsley's mild-flavored botanical formula makes it a pleasure for a man to wash his beard as often and as thoroughly as he likes. It also works on mustaches (duh).
Buy a bottle - let us know if it works better than say... Suave.