My wife was recently laid off and will be joining my health insurance plan that I have through my employer. She's on a visa, so will not be claiming any unemployment benefits. Since my insurance will be more expensive after adding her, she will be paying the difference out-of-pocket every two weeks. Can she use her HSA balance to pay me that money?
No - Insurance premiums are not eligible HSA expenses except in certain circumstances (one being receiving unemployment benefits).
From the IRS:
You can’t treat insurance premiums as qualified medical expenses unless the premiums are for any of the following.
Long-term care insurance.
Health care continuation coverage (such as coverage under COBRA).
Health care coverage while receiving unemployment compensation under federal or state law.
Medicare and other health care coverage if you were 65 or older (other than premiums for a Medicare supplemental policy, such as Medigap).
The premiums for long-term care insurance (item (1)) that you can treat as qualified medical expenses are subject to limits based on age and are adjusted annually. See Limit on long-term care premiums you can deduct in the Instructions for Schedule A (Form 1040).
Items (2) and (3) can be for your spouse or a dependent meeting the requirement for that type of coverage. For item (4), if you, the account beneficiary, aren’t 65 or older, Medicare premiums for coverage of your spouse or a dependent (who is 65 or older) aren’t generally qualified medical expenses.