A B350 CREW; DEPARTING MMU; OVERSHOT THEIR ASSIGNED SID ALT WHEN DISTR BY A FLAP PROB.

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UNCOMMANDED FULL FLAPS CAUSED AN UNUSUALLY 'FLAT' ROTATION AND CLB. WHEN THE GEAR IS RETRACTED WITH FULL FLAPS; THE GEAR WARNING HORN SOUNDS AND CAN ONLY BE SILENCED BY EXTENDING THE GEAR. I WAS MANAGING THE AIRSPD BELOW VLO AND VLR AS WELL AS FLAPS EXTENDED LIMITS; EXTENDING THE GEAR (TO SILENCE HORN); AND TRYING TO FIX THE FLAP SIT. THIS ALL OCCURRING WHILE FLYING THE VERY TIGHT CONSTRAINTS OF THE MORRISTOWN 5 DEP WHICH CALLS FOR A CLB TO 2000 FT AND TURN TO 160 DEGS AFTER PASSING 1700 FT. IN ALL OF OUR BUSINESS; WE LEVELED AT 3000 FT -- 1000 FT ABOVE THE SID ALT. ONCE THE FLAPS CAME TO APCH; WE RETRACTED THE GEAR WITH NO HORN. HOW THE PROB AROSE: UNCOMMANDED FLAPS AND GEAR HORN DISTR US FROM OUR ALT AND WE CLBED ABOVE IT BY 1000 FT AND LEVELED. CONTRIBUTING FACTORS: DISTRS OF ABNORMAL FLAPS (UNCOMMANDED) AND GEAR WARNING HORN; MAINTAINING LOWER THAN NORMAL DEP SPDS; AND ATTEMPTS TO RECTIFY FLAP SIT. CLBING WAS QUICKEST WAY TO KEEP SLOW ENOUGH TO COMPLY WITH LIMITATIONS WHILE REDUCING PWR. ATC ASKED US TO CONFIRM OUR ALT 3000 FT AND WE DID. HE SAID WE NEEDED TO REVIEW THE MMU 5 DEP -- 'THE ALT IS 2000 FT.' ATC ASKED US TO MAINTAIN 3000 FT AND SHORTLY CLBED US TO 6000 FT. NO TFC CONFLICTS AROSE ACCORDING TO THE SUPVR WHEN I CALLED HIM LATER ON THE TELEPHONE.