Two brothers, 30 and 33, and the wife of the oldest, all from Limassol, were remanded in custody for eight days on Saturday in connection with possession of around 28 kilos of drugs.
The woman, 31, is held at an unspecified venue where she can take care of her 18-month-old baby.
Police said there were seeking a fourth suspect whose identity they have not yet confirmed.
The court heard that the home of the 33-year-old, who is a police officer at the British bases, had been put under surveillance after a tip off that he and his brother had stashed a large quantity of drugs.
On Friday afternoon, the 30-year-old was seen arriving in his car, loaded with boxes. He parked it, rear first, in the home’s parking.
When the drug squad appeared, the suspect tried to escape but he crashed into two police vehicles, seriously injuring one officer.
A search of the suspect’s car found five large cardboard boxes containing around 26 kilos of cannabis, 860 grammes of cannabis resin, and 1.1 kilos of methamphetamines.
Officers then searched the house with the wife’s permission, finding close to half a kilo of cannabis and a precision scale.
The 33-year-old was arrested upon his arrival home.
Police said they were seeking a fourth suspect whose full identity was unknown.