I think what you will find is that you will have to study the datasheet for the AVR chip and learn how the various options for parity checking are enabled and how actual received parity errors are detected and signaled. Once you do understand how the underlining hardware functions, then you have to see how you will go about either modifying the existing hardware serial library to integrate this new 'feature' or write your own custom serial library. The fact that the existing hardware serial library utilizes buffered interrupt driven on received characters makes this not so simple a feature to implement.
First you have to ask yourself what you want to happen if and when a character is received that has bad parity detected? Your choices are fairly limited, either just throw the character away or via a protocol you work out with the sender of the characters, send them a signal that you received a bad character and to resend the character or the complete message. So you see it can get quite complex quite quickly and it is very much just a part of the overall serial protocol you wish to utilize between the sender and receiver of serial data.
Good luck;
Lefty