How can I index PDFs that reside on a Unix server?

No, not at all. "Indexing" is a stange and inconsistently used term for this connection. What I assume you really want is a search engine that includes PDF as well as HTML content. The term "indexing" can be taken to mean "taking all of the text in a file and adding it to the words available for searching".

Acrobat uses "indexing" to mean specifically creating a set of files used by Acrobat itself for searching multiple PDFs. But this is a local file thing, not a web thing. Indexing in this way PDF files that are to be used on the web does no harm, but equally, no good.

There are two main approaches to web search engines.

1. Local. Software runs on the local machine, and reads files on the web site. Makes some kind of file, perhaps called an index. Local software on the web server uses this information to show you results.

2. Remote. Google is an obvious case of this. Visits web sites ("spiders") to read files, makes its own "index" and searches across sites.

Google (and other search engines) are often thought of only as a way of searching the whole web. But they can be used to search single servers in their list of the whole world, as in https://www.google.co.uk/search?q=indexing+Pdfs+site%3Aadobe.com

An interesting variation of this, which was on sale a few years ago, is the "google appliance" for use on private networks (intranets). It sat on the local network and did google-like things but only with the local network. Then there was a "local google" for all the local machines.

One more thing: your customers aren't likely to find it satisfactory if they have to search PDFs and search HTMLs with a different engine.