The C# (and other .NET compilers) treat an assembly as the smallest unit they will emit. You'd have to change that to some semblance of "object files" instead along with a "linker" step afterwards to allow for an assembly to be made up of different languages. Again, this is how the
compilers work currently, so MSBuild (well, the default targets) just go along with this. This has nothing to do with MSBuild, which basically just tracks items, properties, targets, and tasks. It doesn't care about the semantics of all that.
Or, you know, use ILMerge, which is pretty much the equivalent of the JS bundlers you mention. With some custom MSBuild targets you should be able to create a project file that contains C# and F# files, both of them compile to intermediate assemblies (although you can't have circular dependencies between both), and a step afterwards merges the assemblies into the actual one.