The EMP burst will most likely be generated by a large blast. A nuke, for example, that would make a large ionizied fireball. Anything in the area will be affected by the EMP but at a sufficient distance, hundreds of miles away, your communication devices will survive and might be able to use the residual ionized gas as a reflecting surface. This would not be repeatable but it would be possible. Meteor bursts happen all the time and amateur radio enthusiasts pick up skips from hundreds to thousand of miles away by bouncing off the trails. Again, it works but is not a reliable method.
An easy reliable method is EME (Earth Moon Earth) which uses the moon as a reflector. You need good antennas and high power but that method is reliable when the moon is visible to both parties. Of course you can use satellites, uplink and downlinks, but for this Q I am assuming that is to be avoided.
@ETpro. I too think it would be pointless (impossible?) to try encoding a signal in the EMP. I’d use it as a reflector.