Air carrier flight crew reported while flying ILS they overshot two crossing restrictions resulting in an unstable approach and were notified of the deviation after landing safely at the airport.
Synopsis
Air carrier flight crew reported while flying ILS they overshot two crossing restrictions resulting in an unstable approach and were notified of the deviation after landing safely at the airport.
Narrative
We were off of our arrival and receiving radar vectors for ILS XXC. We were given a clearance direct to ZZZZZ and cross ZZZZZ at or above 7000. Once we read back the clearance we noticed ZZZZZ had 9000 as a restriction on it so we verified with atc the at or above 7000 at ZZZZZ. ATC verified our read back so we set 7000 in the MCP and descended to 7000. We crossed ZZZZZ at or above 7000 and continued in on the localizer. Soon after we crossed ZZZZZ were cleared for the approach. Once cleared we set the final approach fix altitude in the MCP of 2200. Tracking the localizer inbound we noticed that the aircraft was beneath the step down altitudes passing ZZZZZ1 below 7000 and ZZZZZ2 below 6000. We then reset the MCP to 5000 so it would level off prior to ZZZZZ3 and pick up the glideslope from there. We leveled and picked up the gs at 5000 at ZZZZZ3 and continued the approach. The rest of the approach and landing was normal. After landing we were taxiing in and told by ground of a possible pilot deviation. After parking and completing our flight we called ATC via the number given and told what happened. They said we were beneath the step down altitudes on the approach and that they would further investigate and be in touch. From all of this I have learned to verify that the step down fixes are being honored on these ILS approaches and I plan on accomplishing this by intercepting the GS at whichever altitude they clear me at for the approach. Especially on these long ILS intercepts with multiple step down fixes.
Second reporter narrative
We were given 7;000 at ZZZZZ and cleared for approach to 27C. I questioned the altitude because it was 2;000 feet below published. After ZZZZZ; I set 2;200 feet for the final approach fix. At 5;500 I realized we were below glide path and leveled at 5;000 to intercept glide path. However we crossed ZZZZZ1 below 7;000. The confusion was that we were cleared below the first two fixes of the approach when cleared for the approach.
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Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.