A319 Captain reported communication system malfunction during takeoff that necessitated using the jumpseat plugs to communicate.

Narrative

On takeoff; sometime over 100 knots; we lost all communication with each other through the intercom as well as the ability to transmit out to ATC. I pulled off my right ear cup and yelled to the fo I lost my intercom I'll be yelling. We hit v1 rotate right about then as we only weighed 121;000 lbs it all happened very quickly. As the fo rotated one of us identified that we had lost auto thrust as we had an ECAM. I don't think we got a master warning or caution for this. Neither of us remember cancelling one on the ground or in the air.We complied with tower instructions and squawked 7600; acknowledged instructions by identing as we switch to departure control. The multiple radio calls and not knowing what was wrong with the airplane were dangerous distractions. We continued the departure procedure; turned the auto thrust back on; leveled the plane at 5000 feet; and turned the autopilot on. Ran the after takeoff checklist.The FO said I have an idea; let me try something; and asked me to take the flight controls. I did. He then unbuckled his seatbelt; spun around in his seat; and plugged into the jumpseaters plugs and was able to reestablish ATC communications through ACP (Audio Control Panel) 3. We continued the flight with me as PF and him reaching overhead to transmit.We texted dispatch to tell them about the loss of communication. The rest of the flight went normally aside from only having one working radio configuration. The thought crossed my mind about returning to ZZZ but I did not verbalize it. Dispatch did not suggest it either so we did not consider it. I did not was to return to ZZZ with only one working radio and partially single pilot as the FO was reaching over his head with his left hand to talk to ATC so I was making all changes to the FCU (Flight Control Unit) myself including altitudes with his verification. When we put the gear down for landing I hearda click in my headset the made me think the intercom/Acp had come back to life; but no it was still broken.Upon arriving in ZZZ1 all ACP functionality returned with the transfer to ground power after engine shutdown. I talked to the previous CA who told me the same loss of communication happened on the previous TWO LEGS (but upon landing) so the fixes" had obviously not worked. Furthermore; we had additional writeups now on this leg like the auto thrust failing; rudder trim limit failure and ADR (Air Data Reference) class two message. So the problem seemed to be getting worse. The previous CA told me they heard clicks in their headsets as well when their malfunctions occurred.Two air carrier mechanics came to ZZZ1 and did all the same things that did not fix the plane the first two times when the night before Maintenance Control told me they were going to replace the LGCIUs (Landing Gear Control Interface Unit) and investigate for faults in the air/ground logic system. They didn't. And then Maintenance Control gave us a good maintenance release and pressured me to fly the plane. The dispatcher and I both refused the plane; the Chief Pilot was on the conference call as well."