You can't directly, because as you say the sphinx index, and the database live within different 'systems'.
So the 'join' is happening in your application. Sounds like you are already implemening what is effectivly a join.
But there are two alternatives if you really dont want to continue with that system,
1) SphinxSE. Its a fake mysql storage engine, when you make a query against the virtual table, a query is made in the background back to sphinx index, and the results of the query are presented as a table, to mysql. Now because its a mysql table, mysql then join it with the database table(s) to present resultset, combinging the query and the data. (there is still seperate systems, but mysql implements the joining logic)
2) Attributes. Can store data in the sphinx index, alongside the full-text index. Sphinx can return the attributes in result sets. In this way you avoid the need for the join, because you get the search results along with the data (which you would of got from mysql) in one go.
(in this way you create one big 'normalized' index)