TAE9141: What you described was/is quite common at my carrier and is generally caused by a poor understanding of Vnav. Assuming VNAV ALT works the same as the B777/B787, here is how I taught it:
Think of the VNAV ALT function as nothing more than an MCP selected vertical constraint to your FMC programmed vertical profile. Another way to think of VNAV ALT - when annunciated, you have a conflict between your FMC programmed cruise (or final descent) altitude and the MCP altitude window.
When you load the FMC as part of preflight duties, you will have entered a CRUISE ALT on your PERF page (assuming of course it’s identical to the big Boeings). The FMC will create an optimum climb IAS/MACH to get you to your FMC cruise altitude based on your weight/winds/OAT, etc. But what the FMC can never know are the ATC restrictions to your climb. So, for example, you get airborne having told the FMC that you want to cruise at (for example), FL380. During the climb, let’s say ATC clears you to FL220 due traffic, expect higher shortly. The FMC had no way to know that ATC was going to interrupt your climb, so you have to restrict the FMC VNAV Climb phase by selecting FL220 on the MCP, and VNAV ALT results. So after a few minutes ATC now clears you to your FMC cruise altitude of FL380. To clear the conflict (as described above), you set FL380 in the MCP window, but remember that whenever VNAV ALT is triggered, in our case at FL220, you’re “stuck” at FL220. All that is now needed is one push of the MCP knob to clear the MCP/FMC conflict, and the climb in VNAV will resume. It is not necessary at all to select FLT LVL CHNG, then reselect VNAV, all that captain was demonstrating was possibly a lack of AFDS knowledge.
I’ll recap: If VNAV ALT is triggered during the climb (or descent for that matter) by an ATC required temporary level off, the “conflict” between the programmed FMC altitude and the MCP selected altitude is cleared, once you’re recleared to a higher/lower altitude, by selecting that higher/lower flight level, and pushing the MCP altitude selector knob once.
Works the same in descent, except that an ATC required level off will of course put you high on your vertical profile once you’re cleared lower. So on descent in VNAV ALT when ATC has required a temporary level off due traffic, the conflict between your FMC altitude (could be an altitude on a STAR, or the IAF altitude, whatever) is cleared by selecting lower once you’re cleared, and pushing the knob once. Since you’re high on the profile VNAV SPD will be annunciated. It is not necessary to select FLT LVL CHNG. Either extending speedbrakes to increase your descent rate will descend you back onto the vertical profile, or opening up the speed window while in VNAV, and bugging a higher airspeed will also descend you onto your vertical profile. Once the aircraft is within a couple of hundred feet (as displayed on the VDEV), VNAV SPD will be replaced by VNAV PATH.