can't add/search attachments when using Datasource: Multiple

I would like to be able to create a single index that includes the content of nodes, the content of taxonomy terms, and the content of files attached to nodes.

I can successfully search the contents of attachments, and I can successfully search the contents of nodes and taxonomy terms in the same index, but I can't seem to get attachment contents into the same index with the nodes and terms.

If I create an index with Datasource = Content, I see Attachment fields on the Fields tab. I can choose to index them, and when I build a search in Views and search for a word found inside an attached PDF, for example, the search is successful and the file and its related node appear in search results.

However, that index doesn't allow me to search terms.

If I create an index with Datasource = Multiple Types, and add Content, Term, User, and File, I don't get Attachments on the Fields tab. I've tried adding lots of things from the Add Related Fields widget (including Content » Files » The file), but I can't find any way to add the content of the attached files. Unsurprisingly, searching for a word from one of the PDF files does not return any search results.

Is there any way to get Attachments fields to show up on a Multiple Types index, so I can search the contents of nodes, terms, AND file attachments?

Thank you!

Kristi