class bidict(dict):

    def __setitem__(self, key, value):
        super(bidict, self).__setitem__(key, value)
super(bidict, self).__setitem__(value, key)

def __delitem__(self, key):
    super(bidict, self).__delitem__(self[key])
super(bidict, self).__delitem__(key)
Поиск ключа из значения в словаре Python: