I didn't say the C++ modules are compiled with a C compiler. You have to use a c++ compiler to do that, such as g++, Dev-C++, VC++ 6.0/7.0, and many other c++ compilers. c++ compilers can compile both c and c++ modules, and it knows how to compile by the file extension (*.c for C code and either *.cpp or *.cc for c++ code). Many c++ compilers have additional options to recognize other file extensions.
If you want to link both C and C++ into the same executable, then yes, the C runtime libraries will also be linked into the program.
[edit]The above assumes that the source code for all *.c and *.cpp files is available and can be modified as needed. In OP case, I don't think he does -- it appears he may be trying to call c++ library functions from c, which as you said before, cannot be done.