I addded the project root of my python project to the PYTHONPATH. Now the import of my modules works in the CLI of python bot NOT in a python script. 
How can I fix that?
Call your script with -v option.

python -v yourscript.py

This will trace all the import statements and look or do grep for your project name. If it's not in that, then either it's not at all added to your python path or you're running different python interpreter.
Relative import works on CLI but not in script