Date: 201604
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: Marginal
Weather elements / visibility: Cloudy; Thunderstorm
Aircraft: B737-800
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Reporter organization: Air Carrier
Reporter function: First Officer
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Situational Awareness
Second reporter function: Captain
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Air Traffic Control; Person Flight Crew
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Air Traffic Control Provided Assistance; Air Traffic Control Separated Traffic; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Contributing factors: Airspace Structure; ATC Equipment / Nav Facility / Buildings; Chart Or Publication; Weather; Procedure
Primary problem: Chart Or Publication

Narrative: We were deviating south of course around Thunderstorm activity. This caused Center to say ' I'll be losing you on Radar; fly present heading and intercept [airway] to [fix] direct [fix] Maintain FL320'.  The PF (Captain) put the radial from [fix] into the FMS and we began to intercept it. At this point Center said that he still showed us East of the [airway]; but we lost communication with ATC at that moment before we could verify what radial ATC wanted us to intercept.  We were trying to verify what course ATC wanted; and also were working our way around the thunderstorms. For several minutes; we were unable to contact ATC for clarification. At this time; the Captain said on Center Frequency and on Guard Frequency that he would be 'Exercising Emergency Authority' to deviate around the weather.We were then able to regain radio contact with Center; and Center expressed concern that we were not on [airway]; and then issued us a clearance to climb to 33;000 feet as a precaution to be sure that we didn't get within 20 miles of separation of another aircraft. We reported level at 33;000 feet; and Center was satisfied that no loss of separation had occurred.  Minutes later; he regained radar coverage; and we completed the rest of the flight uneventfully.The difficulty in complying with the clearance to intercept [airway] from two factors: The wording of ATC's clearance led us to believe that we were south of [fix] when in fact we were a little bit south of [fix]. There is a bend in the airway at [fix]; so intercepting the 142 radial; was not accomplishing what ATC wanted. We could not get [airway] to show in the FMS; because we didn't have the anchor point South of [fix].   Our Jeppesen Chart cuts off at the border; and does not show the bend in the airway; or anything South of [fix].This would have been rectified easily with a radial from ATC; but we lost radio contact before we could get one.


Second narrative: ATC starting vectoring us and other aircraft south of our course for weather. This went on for hundreds of miles and we were south of course paralleling our route. The weather continued to build and we continued to parallel course to the south. I noticed we were approaching the FIR. The controller then said we were going non radar and said to continue on our heading of 265 and to join [route].Actual clearance. Never heard of [airway] but found part of it on charts. It extended from [fix] to [fix] intersection. Quickly anchored off of [fix] on fix page then legs. Selected LNAV and thought everything was good not knowing there is a bend in the airway because we don't have the Chart for that on Domestic. There is a chart which we don't carry so didn't see the bend in the airway. ARTCC asked why we were turning when we were still east of course. We said we were joining the airway which we weren't actually. Then we lost contact with him and were headed for weather. [We deviated] for weather and turned back towards the inbound course. We then re-established communications with center. He scolded us and told us to climb 33;000 feet. He said that there could have been a loss of separation but there was not.Chart ZZZ would have helped to see the entire airway.


Synopsis: A B737-800 aircraft deviating for weather was issued a reroute. The crew did not have the charts depicting the route issued to them. The flight did not comply with their assigned route and flew out of radio and radar coverage for a period of time deviating on their own navigation for weather.