Javac allows to inherit a method with one signature from the superclass and a super interface at the same time. 
It is also not a problem if this method is protected in the class and is certainly public in the interface - you just have to override it as public in the subclass.

But for some unclear reasons using the described class and the interface 
as the multiple bounds for a generic type doesn't work.

Here it the minimal test case:

class MyClass {
    protected void foo() {
    }
}

interface MyInterface {
    public void foo();
}

// MixedClass compiles fine
class MixedClass extends MyClass implements MyInterface {
    public void foo() {
        super.foo();
    }
}

// this doesn't compile wit the message
// foo() in MyClass cannot implement foo() in MyInterface
// which isn't correct, because it perfectly can do it in the subclass
public class GenericProblem<T extends MyClass & MyInterface> {

}

This problem is reproducible with the latest JDK 7