A Light Transport flight crew thoroughly briefed the TEB RUUDY TWO Departure but in a miscommunication the non-flying pilot set 2;000 FT in the VNAV and the pilot flying began the climb early. Noise and turbulence added to the confusion and ATC instructed them to continue the climb.

Narrative

Deviation from departure procedure mandatory crossing altitude: RUUDY 2 RNAV Departure from TEB; Part 91 empty leg. (No passenger). Procedure was thoroughly briefed prior to departure. Daytime VFR conditions; gusts & turbulence were in effect with heavy air traffic flow in the NYC area. Problem arose after a level off at 1;500 FT was accomplished 2 NM prior to WENTZ and I called and set 'Next Altitude 2;000 FT'; the crossing restriction for TASCA 2 NM after WENTZ. The pilot flying understood ATC had cleared us to 2;000 FT when I made the callout 'Next Altitude is 2;000 FT; Set' and departed crossing altitude 1 NM from fix. ATC immediately queried altitude and I responded 'leveling off 2;000 FT; returning to 1;500 FT' The Controller replied 'don't do that; continue the climb to 6;000 FT and turn heading 090.' In effect we crossed WENTZ at about 1;850 FT. These events took approximately ten-fifteen seconds to unfold once we left 1;500 FT. Contributing Factors: Turbulence and gusts; loud cockpit noise; the pilot flying was having doubts about the performance of the autopilot and disconnected the autopilot and proceeded to hand fly the aircraft. I (pilot not flying) was heads down in the cockpit and failed to notice the premature climb about 1 NM from fix. Problem was discovered only after ATC queried altitude and no corrective actions were made to descend because ATC re-cleared us to next altitude. Our pilots are trained to set 'Next Altitude' prior to crossing fix; I just completed recurrent training in last month. Maybe our company should revaluate this as an SOP and not teach changing altitude alerter prior to fixes. Further; I think the company should invest in better noise-cancelling headsets for each aircraft to reduce communication errors inside the cockpit.