Common base class + abstract interface class

[nuzzle]

I know that all objects that inherit MyInterface also inherit MyBaseclass, but the compiler doesn't know that. MyContainerclass wants to call methods in MyBaseclass, but it collects pointers to MyInterface classes. I can't make MyInterface inherit MyBaseclass,

You don't want to let MyInterface inherit MyBaseclass but maybe you could let MyInterface define a method which returns a pointer to MyBaseclass? Essentially that method just returns this.

With such a method you can use any MyInterface object as a MyBaseclass object too (as long as it is a MyBaseclass object of course).