Air carrier pilot reported during descent they failed to notice the aircraft descended below a step down altitude. Flight crew recovered from altitude deviation and continued approach.

Narrative

Approaching the ZZZZZ fix; ATC cleared us for the RVAV X XXR Approach. The Pilot Monitoring (PM) asked the Pilot Flying (PF) if he wanted the FAF altitude of 8;100 ft. in the Mode Control Panel altitude window and set it for him. The PM neglected to check that the aircraft was in the VNAV mode before setting the altitude; (the aircraft was descending at 1000 FPM in VSPEED mode). There was a slight distraction about which approach to shoot and as the Crew consulted approach plates and discussed if an ILS or RNAV would be preferred; both Crew failed to notice the aircraft descending below the step down altitude of 9900 ft. at ZZZZZ1 and 12;000 ft. outside ZZZZZ. Being in VNAV mode would have prevented the error. As we turned our attention back to the approach we were flying we noticed our altitude deviation and leveled off. No secondary warnings of Low Altitude were activated; (TCAS etc.) during the entire event and recovery we had the mountainous terrain below and along the approach path in sight; and ATC never called out our altitude deviation. We remained in level flight until back on the approach profile and continued the approach without incident.Suggestions: Better automation management; especially in regards to any descent using VNAV through intermediate step altitudes; needs be accomplished. Also; perhaps the PM should not offer to change Mode Control Panel parameters so readily when the PF is still orientating to a new clearance.