If I am asked in an interview to write down some code, should I completely stick with C++ or is it acceptable to "mix" the two to write easy code as it comes to my mind?
That entirely depends on what kind of job you are applying for and which language they expect you to use. Generally, if you are writing C++, it is best to stick to C++ as far as possible. I would however expect every C++ programmer to know at least a bit of C (and vice versa).
I'll explain it: if I'm asked to create a "stack" data type, a C++ class is perfectly suited, while if I need to parse some strings a strtok/sscanf is far easier than STL. On the other hand, if I need a generic container STL and templates are the way to go.
If they expect you to write a whole working data type during the interview, you should be wary. It is good if they ask you about technical details, but if they expect you to spend hours of writing programs during the interview, that likely says something bad about the employer.
If you use scanf(), you have probably made a big mistake no matter if C or C++. You better explain to the interviewer that you are just writing something quick & dirty and would never use scanf in production code. There are many pit falls with various C library functions.
The interviewer shouldn't expect you to remember every function in the C and C++ standard librarier, but they should expect you to know which ones that are blatantly dangerous. gets(), getchar(), scanf(), setjmp() etc.