Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Workload; Time Pressure; Physiological - Other; Communication Breakdown; Distraction
ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Procedure; Weather; Company Policy
Immediately after takeoff. Me and my First Officer (FO) encountered windshear. I am new to the aircraft so everything seemed to happen very quickly. I'll try to give you the facts the best I can.  Immediately after wheels off the ground the windshear alert sounded. We got 3 orals and windshear guidance. The First Officer was pilot flying (PF) [and] I was pilot monitoring (PM). We were going up to 10;000 feet which had been set. During our windshear recovery ATC gave us a new heading and I read back something like the heading and also that we were in windshear recovery and encountering severe turbulence. As we were reaching 10;000 feet; I was telling the FO to watch his pitch and altitude. The FO was doing the best he could with the conditions we were in. As we were passing through 10;000 feet ATC gave us 14;000 feet. We set 14;000 feet. Somewhere in between 10;000 feet and 13;500 feet ATC tried to give us a phone number to call. I told him to standby and we were still in severe windshear and turbulence. About 13;500 feet we exited into better conditions. We were on a reposition flight; the aircraft was light and climbing rapidly. About this time I told the FO to watch his altitude. I said it a few times and tried to assist him to push the nose down. We were unable to level off in time. ATC told us we went through 14;000 feet. We got back down as quick as possible. We got the autopilot on; took down the number from ATC; and made a PIREP.  In the future faced with a similar situation with a thunderstorm approaching the field I'd heavily consider waiting until it passed the field before departing. My thought at the time was several aircraft departed ahead of us took off so I figured we would be OK. Unfortunately that wasn't the case. If I do encounter windshear/significant turbulence in the future on departure I would be much more vigilant at making my call outs of airspeed; pitch corrections; and heading corrections. I would tell ATC to standby windshear recovery and leave it at that until we were completely clear of the conflict. But in hindsight I should have decided to wait it out.
In hind sight I would also consider rejecting the takeoff if the wind is drastically different than reported judging by the corrections required to maintain the Runway Centerline.
An air carrier crew took off into a line of thunderstorms; encountered windshear immediately after liftoff and initiated the windshear recovery procedure. Severe turbulence then continued up to about 13;500 feet. The crew had difficulty leveling at 14;000; due to the aircraft's high rate of climb.