A320 First Officer reports lost communications with ABQ Center and deviates without clearance to avoid weather. It is later discovered that the Captain's microphone jack had come unplugged causing the outage.

Narrative

While climbing above FL180 the departure; the pilot not flying and I noticed thunderclouds nearby. We saw cloud visually; as well as on radar; painting some red in the cloud. The pilot not flying and I discussed and agreed to deviate left (north) of course; for weather avoidance. Three or four times the pilot not flying tried to contact ABQ Center for permission to deviate; with no reply from ABQ. Meanwhile; the frequency was a bit busy with other aircraft checking in; and ABQ Center issuing weather advisories. Faced with the choice of penetrating a cloud returning red echoes; and deviating without clearance from ATC; we opted to choose what we felt was the safest option and deviated left for a short time. We assumed the pilot not flying's radio was dead; so the pilot flying tried to contact ATC with no answer. [We] finally got a hand off from ATC to new frequency which the pilot flying answered. Upon checking in with new ATC frequency we advised ATC of our deviation; and that we were returning on course. At about this time; we realized the pilot not flying's microphone jack had come disconnected; and that's why ATC could not hear us.