FLC OF AN MLG OVERSHOT ASSIGNED ALT DURING DEP CLB RESULTING IN ATC INTERVENTION BY PROVIDING A TURN TO PREVENT A CONFLICT.

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WHILE CLBING OUT OF BOS DEPARTING NBOUND TO BTV; VT. WE WERE GIVEN A CLB FROM 3000 FT TO 4000 FT AND THEN SWITCHED FROM DEP FREQ 133.0 TO 118.25. MY FO WAS FLYING THE ACFT. AS I SWITCHED RADIOS; I NOTICED THAT HE WAS GOING TO OVERSHOOT THE ASSIGNED ALT. ALSO AT THE SAME TIME; I NOTICED THE TFC AT ABOUT 11 O'CLOCK AT 5000 FT. WHEN I CONTACTED DEP; I MISSTATED THAT WE WERE CLBING TO 5000 FT. WHILE CORRECTING MY FO TO LEVELOFF AT 4000 FT; THE CTLR GAVE US A 5 DEG TURN TO THE R TO AVOID A CONFLICT WITH THE OTHER TFC. MY FO OVERSHOT 4000 FT TO 4400 FT. WE RECOVERED TO 4000 FT. AT THAT POINT; ATC CLRED US ON COURSE. MY FO ADMITTED TO ME HE WASN'T PAYING ATTN. I DIDN'T CATCH IT IN TIME. ALSO; I MADE THE MISSTATEMENT THAT WE WERE CLBING TO 5000 FT. THE CTLR STATED THAT WE SHOULD HAVE BEEN CLRED TO 4000 FT. NO FURTHER DISCUSSION WAS MADE BTWN US AND THE CTLR; THEN WE WERE CLRED TO 12000 FT AND HANDED OVER TO ZBW. MY FO STATED TO ME LATER THAT HE WAS FATIGUED AND DID NOT GET A GOOD NIGHT'S SLEEP THE NIGHT BEFORE. ALL OF OUR COMPANY RUNS ARE SCHEDULED FOR MINIMUM REST AND SOMETIMES FATIGUE DOES PLAY A FACTOR IN OUR PERFORMANCE. I WAS WELL RESTED; BUT DID NOT CATCH THE CLBING TREND IN TIME BECAUSE I WAS HEADS UP LOOKING OUT THE WINDOW FOR TFC.