A G550 crew operating in foreign airspace did not clearly understand their altitude assignment even after repeatedly requesting clarification.

Narrative

This situation developed during the initial climb out. During climbout we were issued a climb clearance by local ATC; which both the Captain and I were unsure of. We both believe we were issued a climb to 'five seven; four hundred meters.' We both knew this was an improper altitude assignment; so we queried the Controller again to clarify the assignment with ATC. We both heard the readback as 'climb to 5;700 meters' which we read back verbatim; then climbed to 5;700 meters. A few minutes later the same Controller issued a nearly 90 degree right turn; and told to 'maintain level.' Again we read back the new clearance and executed the approximately 90 degree right turn. A few more minutes elapsed were then instructed to turn left to a heading of 360. After a few moments; we were re-cleared direct to a NDB; then; on course. The Controller then asked what our altitude was; and of course we responded '5;700 meters assigned' and heard a garbled transmission regarding 5;400 meters. Startled; we attempted to verify our assigned altitude of 5;700 meters; but before we got a response; a new Controller took over and issued a new climb clearance to a higher flight level. At no time was there a separation error as verified by onboard TCAS. Both the Captain and myself agree that a combination of very poor ATC transmission quality coupled with the language problem could have placed us in a situation an altitude deviation could have occurred; in spite of many attempts to clarify our climb instructions with Chinese ATC. If in doubt; ask for a readback of an ambiguous clearance; no matter how many times it takes; until both crew members are sure they understand the ATC clearance they have been issued. Also; it is vital that proper ICAO phraseology be used when operating in countries where the local language or dialect can impose a challenge to the most seasoned crews.