Air carrier First Officer reported the communication system failed during cruise; including cabin communications. Communications were relayed to ATC through Dispatch and the flight continued to a safe landing.

Narrative

En-route from ZZZ to ZZZ1 in cruise at FL360 with approximately 1 hour remaining in the 3 hours and 2 minute flight we began to hear an audible clicking noise every so often over the COMMS system. At first we were not sure what was causing but did not to indicate any issues with communication. Then soon later it became aware from both flying pilot and non flying pilot that were no longer capable of hearing any transmissions from ATC. We tried calling on both Comm 1 and Comm 2 but both were having issues and hearing the audible sounds whenever attempting to transmit. Afterwards we began making numerous attempts to regain contact via both radios; handheld mics; different headsets; communication plug ins including the jump seat panel as well as the backup radio. None were successful; however we were able to maintain a form of communication via ACARS with dispatch and communicated our situation with them and requested they loop ATC in. Per the FOM after seeing as we had lost communication we squawked 7600. We attempted to communicate the situation to the Flight Attendants but it seemed the problem had also affected our ability to communicate with the Flight Attendants. We then used alternative means to communicate with them with notes passed between the door. Relaying our situation and plan; as well as remaining flight time and to secure the cabin and prepare for landing. They did an excellent job of keeping the cabin operations routine and the issue completely unknown to the passengers. Dispatch continue to relay via ACARS additional frequencies to try along our route as well as instructions from ATC to start a descent to 12;000 feet at ZZZZZ en-route to ZZZ1. Dispatch also relayed additional actions to attempt to regain communication. At this point our dispatcher requested priority handling on our behalf. Shortly before reaching our descent point at ZZZZZ the non-flying pilot was able to regain radio contact via the backup radio and establish communication with ATC. They proceeded to give us the same direction we had from dispatch to descend and maintain 12;000 feet. We then proceeded the remaining of the flight in full contact with ATC. We continue to fly the ZZZZZ1 RNAV arrival as planned and then proceed to request the RNAV RNP Z Runway XX. ATC cleared us as requested and proceeded along with a clearance to the approach and to land on Runway XX at ZZZ1 prior to reaching the IAF of ZZZZZ2. We flew the approach to a safe landing on Runway XX and proceeding to the gate without anymore issue and being in contact with ATC ever since regaining contact with them. Upon reaching the gate we deplaned without issue as normal. It was truly an excellent performance working the problem from both pilots and flight attendants. As well as communicating between flight attendants. Overall was a great team effort between; pilots; flight attendants; dispatcher; and ATC to work the problem and conclude with flight safely.