LR31 crew exceeded 1500 FT prior to the TEB 4.5 DME on the TEB5 departure.

Narrative

The TEB5 departure was climb on runway heading to 1;500 FT then a turn. Once passing 4.5 DME from TEB climb and maintain 2;000 FT. I reviewed the departure and waited on our passenger. Our passenger arrived early and we jumped in and started taxiing. The taxi to the runway was very short. Tower immediately cleared us for takeoff. I looked at the departure loaded into the FMS and it showed a point (1;500 FT) and then a line to the next point. I questioned the altitude that we were cleared to and my partner looked at the chart and said 2;000 FT. I was not sure; but considering we were cleared and he knows what he is doing; I let him reset 2;000 FT on the altitude preselect. We climbed out and reported 1;700 climbing to 2;000 FT. The response was 'OK...you are on the TEB...since you are there climb and maintain 10;000 FT.' We looked at the departure and realized that we needed to stay at 1;500 until 4.5 DME. What caused this was the fact that we were rushed due to the immediate clearance to depart and the fact that the EFB that we use is hard to read (familiarity with the FMS).