XOR light switch with two switches and a relay
It sounds like you have what we call a "three-way" switch arrangement. That is two SPDT switches. You can replace one of those switches with the SPDT relay (conformance with whatever your local electrical codes require is not considered in this answer). 

If you wish to retain both the two existing switches, it cannot be done with a SPDT relay- you will need  a DPDT relay or two SPDT relays wired to work together. 



In this case the DPDT relay is wired as a reversing relay and replaces the "4-way" switch in the above diagram (from here). 







simulate this circuit &ndash; Schematic created using CircuitLab