apache & iis are just http servers—so, no, one is sufficient.
that said, it depends on what application server you wish to interact with, vis a vis php/dot net/ruby/python/java etc.
you can pretty much run any variant of app. server behind any http server but you will find some play better with each other
anyway, lose apache if you can, it's a resource hog; have a look at other open source alternatives like nginx/lighttpd or litespeed which is commercial but with a limited free license