It's quite easy to host multiple ASP.NET projects on a single Azure Web Role (tutorial) but is it possible to use a single Web Role to host both ASP.NET and node.js projects?
Yes this is possible, using 2 different solutions:
You can have a background startup task that runs node.exe with the required parameters. For your ASP.NET application nothing changes, the only thing you'll need to do is include the node files in that project and reference that directory when launching node.exe
Use iisnode. This allows you to run your node code through an IIS HttpModule which brings some extra nice features with it (quoting Tomasz Janczuk):