Commercial Fixed Wing
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 57; Flight Crew Total 5906; Flight Crew Type 2235
Workload; Training / Qualification; Distraction; Communication Breakdown
Deviation - Altitude Overshoot; Deviation - Altitude Crossing Restriction Not Met; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors
During our preflight the Captain and I discussed how recently we had each flown.  I had not flown for about 5 weeks and the Captain had just done landings class at training after not flying since March; as I recall.  This was the Captain's first trip since then.After takeoff; Captain was hand flying the airplane and I was performing PM duties.  We were on the ZZZZZ2 departure and I had checked in with ZZZ Departure.  They told us about a storm directly to our south that other flights were having to leave the departure route to avoid.  ATC said we could continue to the west and turn to a 150 heading when able.  After looking at the radar return I acknowledged the instruction and added we would have to go about another 10 miles west.  ATC acknowledged and cleared us to climb to 12;000 feet.I should also mention this was in a very compressed time line.  Tower turned us over to Departure; I was doing the After Takeoff Check and making FMC modifications under the Captain's instructions; and checking in and talking with ATC.  The plane was also very light; so we were climbing rapidly.  I was interrupted three times while trying to read the After Takeoff Checklist and I think we were nearly at 10;000 feet by the time I was able to accomplish the checklist.  I guess; what I'm trying to say is; I felt that I was very busy; and surprisingly so.  ZZZZZ can get busy; apparently even now; but the thunderstorm and the communication and coordination involved with that probably took us to task saturation.After being cleared to 12;000; we got another frequency change and ATC cleared us to 14;000 feet.  I set it in the MCP and saw the flight director was still in LNAV and commanding a left turn.  I asked if Captain wanted HDG SEL and Captain did which I accomplished.  ATC then asked us about the turn to the south and I answered we still were going to have to go further west; but the tops were lowering and I thought the turn could be made soon.  ATC then amended our cleared altitude to 12;000 feet again.I reset the MCP again and got acknowledgment from the Captain.  ATC then cleared us to go direct to ZZZZZ1 when we were able.  I put it in the FMC to see how the course looked compared to the radar return.  I looked out the window to see how the tops were looking.  I heard the altitude alert chime then looked at our altimeter and saw we were climbing through 12;000 feet.  I immediately exclaimed we were cleared to 12;000 feet and I think the Captain swore and immediately reversed the climb.ATC then informed us we were cleared to 12;000 feet.  I re-acknowledged the altitude clearance and we descended back to 12;000 feet.  I don't think we got above 12;600 feet.I wish I could remember when we were re-cleared to 12;000 feet; because I don't remember hearing the approaching altitude alert chime.  I think the altitude may have been above 11;000 feet so we were already within the 900 foot alert window.  When the chime did sound; I thought it was the 900 feet to go; but it was really the 300 foot off warning.
We were on the departure and had been told to maintain a heading due to weather. Altitude clearance was to 14;000 feet. A series of instructions came regarding weather deviations; cleared to a fix when able; etc. Somewhere in here our altitude clearance was modified to 12;000 feet. We were discussing our strategy with regards to getting back on course when the FO realized and announced I had passed 12;000 feet and was at 12;400 feet. I still had 14;000 feet in my mind as our clearance limit. Neither of us remembers an altitude warning horn sounding as we passed 11;000 feet. We both felt task saturated at the time. Neither pilot has been actively flying over the past several months; and currency/recency of experience was absolutely a contributing factor.
Air carrier flight crew reported a track and altitude deviation during departure.  Flight crew cited task saturation and lack of flying were contributing factors.