At a very theoretical level, this is possible. As some people have noted, you can use different methods to have multiple class libraries in one application, each of which is written in a different programming language. At the end, he imitates the experience of writing a single application in several languages. I would say that most of the time this should be enough.
There is also a small, well-known feature of .NET and the CLR called the "net module". See this blog post for an explanation of network modules and assemblies (and even assemblies with multiple files!).
Having said all this, my first recommendation would be to simply choose one language and stick to it. If this is not an option, having multiple assemblies is a good choice. Using the App_Code trick mentioned by Florim will allow you to store all your files in one project, even if several assemblies on ASP.NET will be created on ASP.NET (you will never see them).
If you have problems with having multiple assemblies, rather than with multiple projects, then it would be helpful to find out what the problem is. ASP.NET projects, one way or another, are almost always compiled into multiple assemblies. There are tricks to avoid this, but they are rarely used (e.g. aspnet_compiler and aspnet_merge).
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