Eliminating multiple inheritance

As I'm sure someone else will comment soon (if they haven't already), one good OO principle is "Favor composition over inheritance". From your description, it sounds suspiciously like you're breaking the Single Responsibility Principle, and should be breaking down the functionality into separate objects.

It also occurs to me that Python supports duck typing, which begs the question "Why is it so important that all the classes have a common base class?"

I think your requirements are over-simplified, since in a real situation, you might have students with their own accounts to handle billing even if they are minors who need parent contact information. Also, you might have parental contact information be different from billing information in an actual situation. You might also have adult students with someone else to bill. BUT, that aside - looking at your requirements, here is one way:

classes: Person, BillingInfo, StudentInfo.

All people are instances of class Person...

class Person:
    # Will have contact fields all people have - or you could split these off into an
    # object.
    parent        # Will be set to None for adults or else point to their parent's
                  # Person object.
    billing_info  # Set to None for non-adults, else to their BillingInfo object.
    student_info  # Set to None for non-student parents, else to their StudentInfo
                  # object. 

Checking the fields will allow you to create lists as you desire.

One solution is to create a base Info class/interface that the classes ContactInfo, StudentInfo, and BillingInfo inherit from. Have some sort of Person object that contains a list of Info objects, and then you can populate the list of Info objects with ContactInfo, StudentInfo, etc.