No, you can't. An assembly/project (each project compiles to 1 assembly usually) has to be one language. However, you can use multiple assemblies, and each can be coded in a different language because they are all compiled to CIL.
It compiled fine and didn't complain because a VB.NET project will only actually compile the .vb files and a C# project will only actually compile the .cs files. It was ignoring the other ones, therefore you did not receive errors.
Edit: If you add a .vb file to a C# project, select the file in the Solution Explorer panel and then look at the Properties panel, you'll notice that the Build Action is 'Content', not 'Compile'. It is treated as a simple text file and doesn't even get embedded in the compiled assembly as a binary resource.
Edit: With asp.net websites you may add c# web user control to vb.net website