Dear babar,

You haven't mentioned the supply you are using for uC and relays and the load being drived by the relay.
I am using four relays and 2 uC in single board having single source of supply i.e. 12VDC to 5VDC, and relays are driven by 12VDC and have never faced this kind of problem.
A 0.1uF cap across vcc and ground of ULN as a decoupling cap can help also.

Harjit