To summarize, one has to set different application pools in IIS for the two applications to debug.
Here is a rough instruction, given that both applications have been deployed to IIS once within Visual Studio.
- Open the Internet Information Services (IIS) Manager
- Click Application Pools on the left pane
- On the right pane add another integrated application pool, let's name it Second ASP.NET 4.0 Integrated
- For one application, open the Advanced Settings...
- In the properties view finally select Second ASP.NET 4.0 Integrated as the application pool
This way the applications should be debuggable in parallel because each Application Pool spawns a new operating system process to which a separate debugger can be attached.