For all of you who stumble upon the same kind of problem (like I did). There is a fairly new Jenkins plugin available that does exactly what is desired here: display a dependent set of drop-downs, updating dependent boxes when a main box changes selection.

For your job you just need to follow the following steps:
Install "Multiselect Parameter Plugin"
The "multiselect parameter plugin" can be installed from Jenkins plugin management, the documentation is available on its Jenkins Plugin page.
Add new parameter
- Use "Multiselect Parameter" type
- Set name to a sensible value
- give a short description
- configure like shown below:
H,Main option,Dependent option V,SELECTED_MAIN,SELECTED_DEPENDENT C,A,Blue C,A,Green C,A,Yellow C,B,Black C,B,White C,B,Grey
Use selected values
When you run "build with parameters" in your job, the following boxes are displayed for selection:

In your build script you can simply use the configured environment variables SELECTED_MAIN and SELECTED_DEPENDENT, which contain the selected values from both select boxes.