MD-80 Series (DC-9-80) Undifferentiated or Other Model
Air Traffic Control Fully Certified
Communication Breakdown
Conflict Airborne Conflict; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance
Procedure; Human Factors
A MD80 called us climbing out on the departure. My trainee RADAR identified the MD80. The next transmission was for the MD80 to 'climb unrestricted maintain 11;000'. The MD80 read back 'unrestricted maintain 11;000'. The next transmission was to the MD80 'traffic 12 o'clock; 20 miles turning northbound a Boeing 737 restricted above you'; the MD80 replied 'traffic in sight'. My trainee instructed the MD80 to maintain visual separation from that traffic and the MD80 read back we will maintain visual separation. The MD80 busted his altitude and at 11;300 my trainee turned the MD80 to a 180 heading for traffic and asked the MD80 to verify they still had the B737 in sight and were maintaining visual; the MD80 replied verify that traffic is at our 11 o'clock.  My trainee replied affirmative and the MD80 replied we are maintaining visual separation from that traffic. The MD80 didn't appear to take the 180 heading and was climbing very well so we waited until the MD80 had vertical separation and issued the new altitude and route to fly.
TRACON Controller described a climb above authorized altitude during the application of visual separation.