Regional Jet 200 ER/LR (CRJ200)
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Communication Breakdown; Confusion
Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance
Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors
ATC assigned TBARR 1 STAR where we needed to be above FL200 at TBARR. During a busy phase we were told to descend via the TBARR arrival 35L transition. We began to comply. After a few minutes of preparing for this transition; which was new to us; we were then assigned 'descend via TBARR except maintain FL190 for traffic.'.  It was read back and understood by the pilot monitoring. The pilot flying however took it to mean remain on the course of the arrival but descend to FL190 now. We reached FL190 before TBARR fix going below the advised en-route altitude. Causal factors for the event were busy phase of flight; multiple clearances; misinterpretation of clearance given; and lack of clarification from both pilots of the meaning of the clearance. ATC could clarify the meaning of this instruction with one or two extra words to assist pilots in desired meaning. Pilots could ask for clarification if needed.
Captain reported descending below the charted TBARR crossing altitude; following a misinterpretation of ATC's; 'descend via; except maintain' instructions.