"C/C++" is a valid term for the common subset of C and C++. Even if both are different languages, it's possible to write code which is both valid C and valid C++ (but is a subset of both languages). Usually the goal when writing "C/C++" is to write C code that also compiles in C++ compilers (and this, contrary to popular believe, is a very restricted subset of C, and is almost a 3rd language).

Also, what else would you call yourself if you write both lots of C++ code (for the job) and C code (for fun) ;)