Cameron Mearns, of no fixed address, and Ashleigh Philpott, from Trinity Square in Magheralin, County Down, were arrested after police raided her home.
A defence solicitor said there was an "extremely weak" case against Ms Philpott and added Mr Mearns had raised a "duress defence" after his arrest.
The case was adjourned until 7 August.
Lisburn Magistrates' Court heard that officers from the PSNI's Organised Crime Branch found a 9mm pistol; cocaine estimated to be worth £7,200 and cannabis with an estimated street value of about £10,000 during the raid on 10 July.
The court was told that as police arrived at Ms Philpott's house, Mr Mearns was allegedly taking the seized items out of a car parked in the driveway while his 25-year-old co-accused was in the front garden.
The pair were jointly charged with having the gun under suspicious circumstances as well as drug possession and possession with intent to supply.
They confirmed to the court that they understood the charges against them.
Mr Mearns, 29, did not apply for bail and was remanded into custody.
Police objected to Ms Philpott's bail application but her defence solicitor said there was no forensic evidence linking her to the gun and drugs.
He added that she had a responsible job as a manager of a chain of chemists and has no criminal convictions
During police interviews, Ms Philpott gave two prepared statements where she denied knowing anything about the gun or drugs and claimed she did not take either cocaine or cannabis.
The judge released her on her own bail of £500 until her next court appearance.
A man and woman both charged with having a gun and drugs estimated to be worth more than £17,000 have appeared in court in Lisburn, County Antrim.