“Does an RF 433MHz Transmitter-Receiver pair interfere with an 315MHz RF transmitter receiver pair?”
No it is not posible.
You can try with ‘transceivers’ like Xbee.
If you are looking for a cheap solution, you can use two pairs of 433MHz transmitter and receiver, but both with a different address set. Use HT12E and HT12D encoder decoder pair for each set.