Yes, a couple can apply for a mortgage even if they have a $100,000 credit card balance. The following are detailed instructions:

1. Credit card debt will not directly affect the qualifications for mortgage applications. Banks will evaluate a number of factors to decide whether to approve an application, including the couple's income, credit history, debt levels and employment status.

2. Banks usually calculate a couple’s debt-to-income ratio (DTI), which is the ratio of debt to income. If a couple's income is high enough to cover their current credit card balances and future mortgage payments, they may still qualify for the loan.

3. Couples should provide a stable source of income as much as possible and demonstrate a good credit record during the application process. This will help increase the success rate of your home loan application.

Summary:

Even if a couple has a credit card debt of 100,000, it is still possible to apply for a mortgage. Key factors are the couple's income level, credit history and debt levels. It is recommended that couples prepare well before applying to ensure that they can meet the bank's requirements.

Supplementary information:

- During the actual application process, the requirements of each bank may be different. It is recommended that couples consult with multiple banks to understand specific loan conditions and application qualifications.

- In addition to credit card debt, banks will also consider other debts, such as personal loans, car loans, etc. Therefore, couples should comprehensively evaluate their debt situation and try to reduce unnecessary debt.