Airbus 318/319/320/321 Undifferentiated
Flight Crew Air Transport Pilot (ATP)
Time Pressure; Situational Awareness
ATC Issue All Types; Deviation - Altitude Overshoot; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Procedure; Human Factors
While inbound to Montego Bay our flight planned route (and clearance) was via the Omaxi 3 Arrival. Upon check in with Kingston Center we were cleared to AVRAT intersection; a waypoint on a 12 nautical mile final to runway 07. AVRAT is not on the Omaxi 3 arrival and while it is on the RNAV Rwy 07 approach plate it was not in the FMGC; which had ZAVKI as the first or initial waypoint/fix on the approach. This required us to type it in ourselves in order to comply with the clearance; which we did. Neither [my First Officer] nor myself thought to also type in the 3000 feet altitude published on the approach plate. Once we were handed off to Sangster Approach they eventually gave us a clearance to proceed to AVRAT; descend to 3000 feet and then cleared for the RNAV Rwy 07 approach. While still on a southerly heading and not yet at AVRAT; we armed the approach and the airplane very shortly thereafter began a descent to 2500 feet (the published altitude at ZAVKI). As we were leveling off at 2500 feet Sangster Approach asked us to confirm our altitude; which we did. Approach then indicated that our clearance was to maintain 3000 feet until AVRAT. We immediately climbed back to 3000 feet; completed the approach and landing (in VMC conditions) uneventfully. Neither [my First Officer] nor I heard or received a clearance to maintain 3000 feet UNTIL AVRAT; though that was the controller's intent and the proper procedure; given the published altitude on the approach plate.Given the relative few times that I've flown into Montego Bay (my previous entry being well over a year ago) we should not have allowed the VFR weather conditions to lull us into not paying closer attention to detail and proper procedure.Separate Domestic and International flight divisions would significantly enhance the safety of our flight operations. As for me; I will study the weather; expected arrival procedures and any unusual or unique characteristics in greater detail before arriving in the terminal area of airports where I have minimal familiarity.
Airbus Captain reported descending below a charted altitude on approach into MKJS.