CAPT OF AN ACR MLG OVERSHOT CLB ALT ON DEP DUE TO BECOMING DISTR BY TFC WATCH. DEP CTLR ALSO NOTICED THE OVERSHOOT AS THE CAPT WAS CORRECTING BACK TO ASSIGNED ALT. WHILE CORRECTING BACK; TCASII RA COMMANDED CLB; BUT THE CAPT SIGHTED THE TFC AND CONTINUED TO LEVEL.

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A MIL DEMONSTRATION TEAM WAS HAVING A PRACTICE SESSION AT FAIRCHILD AFB; JUST E OF THE SPOKANE DEP PATH; CAUSING DEP DELAYS. ONCE AIRBORNE; WE WERE GIVEN SEVERAL TURNS AND ALT CHANGES FOR TFC. WE WERE GIVEN A CLB TO 5000 FT AND FLY HDG TO JOIN AN AIRWAY AND ADVISED OF A VFR CHEROKEE AT 10-11 O'CLOCK; LOW. THE AIRWAY GIVEN BY ATC WAS NOT KNOWN TO EITHER COCKPIT CREW MEMBER. THE FO STARTED SEARCHING THE CHARTS. I WAS OUTSIDE LOOKING FOR THE TFC. AT THAT MOMENT; I GOT THE ALT ALERT HORN (OVERSHOOT) AND BEGAN TO CORRECT TOWARD 5000 FT. THE CTLR NOTED THE ALT EXCURSION AND TOLD US TO MAINTAIN 5000 FT. AS I WAS PUSHING OVER TO CORRECT THE ALT I ASKED FOR A REPEAT OF THE AIRWAY NUMBER TO JOIN. AS I WAS SPEAKING AND DSNDING; THE TCASII GAVE AN RA TO CLB. I WAS ABLE TO VISUALLY ACQUIRE THE TFC AND LEVELED AT 5000 FT. OVERSHOOT WAS 300-400 FT. A NEW HDG WAS GIVEN TO JOIN THE FILED AIRWAY. REST OF THE FLT NORMAL. A PHONE CALL TO SPOKANE ATC CONFIRMED THERE WAS NO TFC CONFLICT AS A RESULT OF OUR OVERSHOOT AND NO VIOLATION WOULD BE FILED. THE USE OF THE AUTOPLT IN THIS UNUSUAL (FOR SPOKANE) SET OF CONDITIONS WOULD HAVE ELIMINATED THE PROB.