An A319 First Officer reported receiving ECAM message ENG 1 REVERSER FAULT. They then noticed a discrepancy between the QRH and the ECAM Supplemental Manual; one of which stated 'Crew Awareness'; the other 'Land ASAP'.

Narrative

During climb received ECAM: ENG 1 REVERSER FAULT. Consulted QRH. ECAM had no additional procedures. QRH listed this ECAM message as only 'CREW AWARENESS'. Later; when time permitted and work load lighter; I checked the ECAM SUPPLEMENTAL MANUAL for any additional information. In that manual; the first item listed after ENG 1 REVERSER FAULT was LAND ASAP! That was NOT displayed on ECAM or QRH! After discussing this; we contacted Dispatcher and Maintenance via ACARS asking for information concerning the conflicting information and whether to continue or return to departure airport. Dispatcher and Maintenance asked us to return. Accomplished overweight landing procedures and logbook write ups. Conflicting information between ECAM; QRH and ECAM SUPPLEMENTAL MANUAL. If the ECAM SUPPLEMENTAL MANUAL has inaccurate information; an unneeded diversion and return to field was the result. If that manual is correct; then ECAM AND QRH are inaccurate and require correction. Both cannot be correct.