A CE650 flight crew climbed through the charted altitude on departure out of TEB.

Narrative

I am a Captain on a Citation 650. Our clearance was the TEB 5 departure; Lanna intersection then as filed. Prior to engine start I had briefed the departure; routing; and noise procedures with the First Officer. The first altitude on the departure was 1500 ft MSL until crossing the TEB 4.5 DME. That was the altitude we had selected in our altitude pre-select. After takeoff we performed the recommended noise procedures. Upon reaching 1500 ft we turned to a 280 degree heading and started increasing the airspeed not to exceed 190 kts. I had scanned the TCAS as I always do at these lower altitudes and busy airports for any traffic. It was at this time I realized that our two independent altitude arming systems were captured on the co-pilot's side and the Captain's side was unlatched. I was at 1650 ft as I realized the deviation and by the time I could stop the climb had gone through 1800 ft MSL. We have incorporated into our flight department a new SOP in this aircraft. The call for altitude leveling is now 'two selected' as well as 'two showing ALT hold' by the flying and the non-flying pilot.