According to the IRS, irs.gov/publications/p969/ar02.html, you (and your spouse, if you have family coverage) generally cannot have any other health coverage that is not a Consumer-driven health plan (CDHP). However, you can still be an eligible individual even if your spouse has non-CDHP coverage provided you are not covered by that plan.
You can have additional insurance that provides benefits only for the following items:
- Liabilities incurred under workers' compensation laws, tort liabilities, or liabilities related to ownership or use of property
- A specific disease or illness
- A fixed amount per day (or other period) of hospitalization
You can also have coverage (whether provided through insurance or otherwise) for the following items:
- Dental care
- Vision care
- Long-term care
PLEASE NOTE: Coverage not specifically listed above cannot include payment for or reimbursement for your copays or deductible.