Is it possible to host a asp.net or jsp website using node.js on server side.
If you do an HTTP GET or POST to another ASP.NET or JSP or whatever other type of site on the Node.js instance, then that is fine as a mashup.
If you are asking if its possible to run the .NET and Java code inside Node.js then you must be joking as this would be a terrible idea to run compiled JIT code within a JavaScript environment.