Patrick McDonald (32), his wife Martina McDonald (30), his father Michael McDonald (51) and mother Margaret McDonald (51) were arrested following a three-year investigation, a court heard.
They are facing trial by judge and jury in the circuit court on the charges.
Judge David McHugh remanded the accused on bail to appear before the court again in March for the book of evidence.
The four appeared before Blanchardstown District Court charged with money laundering offences.
It is alleged they operated bank accounts in An Post, AIB and Ulster Bank which were used to conceal the proceeds of crime.
There is also a charge of possession of a Skoda Octavia, which was allegedly the proceeds of crime, at Snugborough Road in Blanchardstown on July 13, 2020.
Detective Garda Gary Farrell said the amounts related to an estimated €220,000 in bank accounts and an estimated €111,000 which was seized in a money box.
The charges arose after a three-year investigation by gardaí, he added, telling the court that "large sums were going through their bank accounts".
Gda Farrell said gardaí had no objection to bail, subject to conditions.
Patrick and Martina McDonald, a couple with four children, were remanded on bail in their own bonds of €100. As part of their bail conditions, they must reside at Allendale Grove in Clonsilla and sign on once a week at Lucan garda station.
Michael and Margaret McDonald must reside at The Mall, Ongar Square, Ongar, and sign on once a week.
Defence solicitors Conor Ruane and Karen Ruane were assigned on free legal aid.
The accused have not yet indicated a plea to the charges.