Is that possible then? I'd always assumed that choosing Swift meant choosing not to use C++ in any way, so had completely rejected it as an option.
The same way you can do it for any other language, thanks to an amazing technology from the 1960s: The Linker.
Programs are built from all kinds of libraries, archives, or modules, depending on how things are named. All the libraries get linked together into the final executable. It doesn't matter if the libraries were built in Swift, C++, C, Assembly, Fortran, or anything else, but they all follow a basic naming system and parameter-passing system and other rules that form a common interface. As long as all the code was compiled to match the same interface -- called the application binary interface -- all the parts will work together.
Although the interface actually predates C, it is often called a C-style linkage or extern "c" or similar.
Swift calls it a "Bridging Header". Google finds this little example among many.