D21 controller described altitude assignment vs. heading mix up that resulted in a near loss of separation event; the controller indicating language barrier as a likely causal factor.

Narrative

A Lear Jet was handed off from the DET City Departure Controller climbing to 8;000. I issued 9;000 to the aircraft. I later cleared the Lear direct to the ANNTS Intersection and heard two separate read backs. Since I was afraid that 2 separate aircraft read back the clearance (after listening to the tapes I believe that both pilots of the same aircraft responded to my direction) I reiterated that the clearance was for the subject Lear Jet. This time I instructed him to 'fly heading two four zero and when you're able go direct to the ANNTS intersection'. The aircraft read back 'direct ANNTS and uh; two four zero'. At the time I believed that this was a correct read back of the heading and departure fix. Although we have not yet spoken with the pilot; I believe now that the pilot intended to climb and maintain FL240. I later observed the aircraft climbing through 10;300 ft. Since there was conflicting traffic at 11;000 and 12;000 I instructed the pilot to descend immediately back to 9;000. I then took action to move traffic that was in front of him at 8;000 in case the immediate instruction caused him to break his altitude assignment on the way back down. Recommendation; I don't know that I would have done anything differently at the time. I honestly believed that the pilot intended to read back the heading and fix he was cleared to. My workload was fairly heavy and I went on to the next task. Perhaps the hesitation in the pilot's voice; coupled with the appearance that English was a second language for him should have raised a flag and I could have taken an extra moment to make sure we were on the same page.