HS125-800 FO OVERSHOT DEP INTERMEDIATE ALT DUE TO DISTR FROM CAPT DURING CLB AND THE SUN'S GLARE IN HIS EYES.

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I WAS DESIGNATED SIC ON THIS TRIP. IT WAS MY LEG TO FLY. WE DEPARTED EMPTY. OUR MISSION TO TAKE THE PLANE TO FTY FOR SCHEDULED MAINT. WE TAXIED TO THE ACTIVE RWY; WHERE WE HAD A LONG WAIT FOR DEP. CLRED INTO POS FOR DEP; WE CONTINUED TO WAIT FOR ANOTHER MIN OR LONGER FOR TKOF CLRNC. OUR INITIAL CLRNC WAS TO CLB TO 2500 FT ON RWY HDG. UPON RECEIVING TKOF CLRNC; OUR ALT WAS CHANGED TO 4000 FT. UPON TKOF ROLL; THE CAPT I WAS FLYING WITH; STATED THAT #2 ENG WAS SLIGHTLY SHORT OF MAKING PWR. HE STATED TO CONTINUE. UPON LIFTOFF; HE STATED AGAIN THAT #2 ENG WAS NOT MAKING AS MUCH PWR AS #1. AT 400 FT; I CALLED FOR FLAPS UP AND AFTER TKOF. UPON BRINGING FLAPS UP AND ENGAGING THE YAW DAMPER; HE SAID THAT IGNITION WAS ALREADY OFF AS I HAD NOT CALLED FOR THE LINE-UP CHK PRIOR TO DEP. HE CONTINUED ON THIS ISSUE AND TO WHY THE #2 ENG WAS NOT PRODUCING AS MUCH PWR AS HE THOUGHT IT SHOULD. DURING THIS COCKPIT CONVERSATION; I WAS CLRED TO CLB TO 5000 FT AND GIVEN A CHANGE IN HDG. HE DID NOT CEASE HIS TALK DURING THIS PHASE OF FLT UPON MY TURN; LIGHT IN THE COCKPIT WAS SOMEWHAT GLARED. I HEARD THE ALT ALERTER; AND BELIEVED I STILL HAD 1000 FT TO CLB. THE DEP CTLR ASKED OUR ALT. I IMMEDIATELY LEVELED AND SAW THAT I WAS AT 6000 FT; NOT 5000 FT. CAPT MISSED THE APPROPRIATE CALL OF 1000 FT TO GO. HE HAD BEEN TOO BUSY CHASTISING ME TO DO SO. THE CTLR THEN CLRED ME TO 10000 FT AND GAVE ME A TURN; THEN A HDOF TO CTR. CAPT STARTED TO TALK AGAIN. I POINTED OUT THAT DEP IS NOT THE PLACE TO TALK ABOUT MY FAULTS. HE REALIZED THIS AND HIS FAULT IN THIS DEV. FIRST I WAS CONCERNED WITH AN ENG PROB; THEN FRUSTRATED WITH MYSELF FOR MISSING THE LINE-UP CHK. HOWEVER; MY CONCENTRATION WAS MOST DISTURBED BY MY CAPT CONTINUING CHATTER. CONVERSATION SHOULD OCCUR ONCE OUT OF CRITICAL PHASES OF FLT. I'M ANGRY AT MYSELF FOR NOT DIRECTING HIM TO CUT OFF THE CHATTER UNTIL WE REACHED A NON CRITICAL PHASE OF FLT.