The 328P hardware UART doesn't support Mark or Space parity. However, as @DrDiettrich pointed out the 328P does have a 9-bit mode. The 328P datasheet I have has a section on "Multi-processor Communication Mode" - it's section 20.9 for me but may be different for you if you have a newer/older datasheet.
I suspect that you can use that to achieve the Mark & Space parity you need for your messages.