Original Post:
How do they integrate these languages?
The way you implement disparate technologies is via compartmentalization into individual packages with some sort of interface to allow the individual units to talk to one another. Typically this would be some sort of server/client relationship such as an API.
A typical example of this is connecting an application to a database. Oracle, MySql, Sql Server have a completely different language set than what the calling application uses.
The Wikipedia entry for
ADO.NET
opens up with
ADO.NET is a data access technology from the Microsoft .NET Framework that provides communication between relational and non-relational systems through a common set of components