There is not much you can do. You can’t deduct any premiums because you don’t pay them. There is a special small business deduction for health insurance, but it must be purchased by the small business owner in their own name, or in the name of the business.
Your partner is taxed on the employer portion of the insurance because the employer is only allowed to provide tax-free benefits to the employee, the employee‘s spouse, and the employee‘s dependents. If you are not a spouse, or a dependent, then the fact that the employer pays part of the insurance must be counted as part of the employee‘s taxable income.
The employee could deduct the imputed income (the employers's share of the premium, added to the employee's income, because the employee pays tax on it) and they could deduct the after-tax share of the premium that they pay (but not the pre-tax share for their own premium), but only if the insurance is covering their spouse, or a dependent, or someone who could be a dependent except for the income rule. As a practical matter, this means that your partner could deduct the after-tax portion of their insurance expenses to cover you, if you lived in their home as a member of their household for all of the tax year, and if your partner provided more than half of your total financial support. This means adding up your total costs, including housing, insurance, food, clothing, travel, entertainment, and everything else, and then determining how much support cost you pay for yourself, and how much support costs your partner pays for you.
Then, the tax benefit of itemizing deductible medical expenses depends on the total of itemized deductions, and the taxpayer‘s total income and other tax facts.
