Date: 201908
Local time of day: 1201-1800
Location: OAK.Airport, CA
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Light Transport
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Climb
Airspace: Class B SFO
ATC / advisory: TRACON NCT
Reporter organization: Air Taxi
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Communication Breakdown; Situational Awareness
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: It appears to be a misunderstanding on the clearance delivered to us for [the] OAK3; OAK departure; because it was 'climb via the SID expect FL 190'; and we understood 'climb via the SID except 190'. Basically; clearance receiving is a function of the First Officer; as he understood EXCEPT instead of EXPECT; he briefed me that we were clear to climb to [flight level] 190. On this departure you have to be at 4 DME above 1;400 ft. and at or below 2;000 ft. and we missed that because of the misunderstanding and crossed the 4 DME about 3;500 ft. To prevent this; we [will make sure] that both pilots have to receive the clearance together and agree [on] what was delivered to us by ATC.


Second narrative: I am writing this report of event in the effort to be transparent and to learn from and to make sure on how not to repeat the same mistake again; to also keep an eye on the Captain's activities as well.It was a flight from OAK to ZZZ. I drove from [base] to meet with the airplane at OAK. Upon arrival at OAK; I did a thorough preflight and all was good. Then I proceeded to pick up the clearance which was clear to ZZZ [via] OAK 3 departure [and] transition as filed; climb via the SID except maintain 190 [expect] 41;000 departure frequency squawk'. I read the clearance back to ATC then loaded the clearance in the FMS; then briefed the Captain twice due to English language deficiency. Also prior to takeoff; I briefed him again as a reminder heading DME and altitude; he said 'I got it'. Took off then since it was extremely [heavy] traffic; I was watching out for traffic at the same time inside to perform my co-pilot duties. Then we received a call from ATC [asking] what was the clearance [that was] given. Then I read it back. Then [they] gave us a heading to fly. Then climb up to [Flight Level] 190 and said to give a call upon reaching 10;000 ft. to which we did.We understand what took place; we have received further training; and we will make sure this event does not [happen] in the future.


Synopsis: Air taxi flight crew reported a communication breakdown between flight crew and ATC regarding departure clearance resulting in a crossing altitude restriction violation.