Nur Shila Kanan, 33, was charged with 12 counts of the alleged offences, while her husband, Basheer Ahmad Maula Sahul Hameed, 33, a mechanic, was charged with four.
Both of them pleaded not guilty to all charges which were read to them before Judge Mat Ghani Abdullah.
On the first four counts, Nur Shila was accused of transferring money totalling RM40,000 from a Malaysian citizen Hue Pui Heng's account into a Chinese citizen Tian Jun Wei's account, and another RM35,000 into Ali Faran Khan's account.
For that, she was charged under Section 4(1)(a) of the Computer Crime Act 1997, which carries a maximum fine of RM150,000 or jail term of 10 years, or both, if convicted.
Nur Shila also faced three counts of using fake documents to apply for a new debit card on Tian's name and to make to two applications for local fund transfer from two savings accounts belonging to Ju Kun, a Chinese national, and Tan Size Hiang, a flight attendant.
She was also charged with using fake Internet Banking Service Request Form on the name of Judy Margaret Lai to acquire the security device to activate the Internet banking service.
For those offences, she was charged under Section 471 of the Penal Code, which carries a maximum jail term of two years, or fine, or both, if convicted.
Nur Shila was also charged with cheating her supervisors, Nor Aini Derus@Mat Rose and Mohd Fazli Mokhtar, into believing that the applications for the new debit card for Tian and Judy were made personally by the applicants.
The offence, under Section 417 of the Penal Code, carries a maximum jail term of five years, or fine, or both, upon conviction.
Nur Shila was also charged with two counts of stealing RM2,530 from Ju Kun's and Tan's accounts, an offence under Section 379 of the Penal Code which provides a maximum imprisonment of seven years, or fine, or both, if convicted.
She also pleaded not guilty to four alternative charges of stealing money belonging to the four victims.
She was alleged to have committed all the offences at her workplace at HSBC Bank in Lebuh Ampang here between May 14 and July 8.
Meanwhile, Basheer Ahmad Maula was charged with four counts of using Tian's debit and ATM cards to withdraw a total of RM7,650 in four transactions.
The offence, under Section 4(1)(a) of the Computer Crime Act 1997, provides a maximum fine of RM150,000 or jail term of 10 years, or both, if convicted.
He also faced four alternative charges under Section 379 of the Penal Code, for stealing money from the same account.
Basheer Ahmad Maula was alleged to have committed all the offences at HSBC Amanah automated teller machine in Ampang Point, Ampang, here, between 10.02am on May 15 and 11.28pm on June 29.
Judge Mat Ghani allowed the accused bail of RM12,000 in one surety each and ordered them to surrender their passports to the court.
He also set Aug 25 for re-mention and ordered the cases to be tried together.
Deputy public prosecutor Ahmad Fadhli Mahmud prosecuted, while the couple, who have three children aged five, two and six months, were represented by lawyer Abdul Hakeem Aiman Mohd.-Bernama