Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Situational Awareness; Confusion; Communication Breakdown
ATC Issue All Types; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Undershoot; Deviation / Discrepancy - Procedural Clearance
Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors
[On departure] we were not issued an arrival into PSP. In flight we were given a reroute to go direct to GLRNO and the SIZLR3 into PSP. At a later communication with ATC we were told to cross GLRNO at 24;000 feet. We started our descent. We were handed off to SoCal who then changed our clearance to 'descend via the SIZLR3.' I armed VNAV and the path captured. On the chart; GLRNO is noted at or above 24;000 feet [and we] crossed above 24;000 feet. SoCal queried us 'would we make the restriction at SIZLR?' which has [charted crossing] altitudes [between] 23;000 feet and 20;000 feet. At that point I realized there was confusion in our clearance. The PIC asked SoCal what was his understanding of our clearance. [The response was] 'To descend via.' It was my interpretation that when given a descend via; unless told to cross the fix at 24;000 feet; you are cleared [via charted restrictions]. I am not sure if it was a poor hand off from controllers or we misinterpreted directions. But from now on I will ask.
[Report narrative contained no additional information]
Medium transport aircraft flight crew reported miscommunication between them and ATC regarding a 'descend via' clearance resulted in a missed crossing altitude.