Sounds like you are trying to perform 9 bit framing using the parity bit settings mark and space. This should be doable under both Win98 and Win2k using the system serial driver. Since both drivers comply with the Win32 API I can not imagine why one "cares about parity" while the other does not. Both should treat parity exactly the same.
LabVIEW (traditional serial vi's) and VISA both make Win32 calls that are routed by the OS to the serial driver specific to the port you are communicating with. In the case of local built-in COM ports, this will be the native OS driver. With regards to handling COM port settings like parity, LabVIEW behaves the same as any other application written to the Win32 serial API.
If you are using the parity bit for 9
bit framing the sequence should be something like the following:
1) Open COM port
2) Set all settings (baud rate, etc.)
3) For each byte written do:
A) Set parity to Mark or Space
B) Write character
C) Wait to allow character write to complete
4) For each byte received do
A) Set parity to Mark or Space
B) Receive character and look for parity error as indication of the value of the 9th bit.
NOTE: Receiving 9 bit data may be tricky if you are also transmitting as you'll be changing parity and it'll be difficult, if not impossible, to know what state the parity setting was in at the instant that a data byte was received.
Hope this helps!