If you are reimbursed under an accountable plan, then reimbursements may be tax free. For example, if reimbursements for your mileage exceed the IRS standard mileage rate, then only amounts up to the rate are tax free; excess reimbursements are taxable.
For 2007, a high deductible health plan is a health plan with an annual deductible that is not less than $1,100 for self-only coverage or $2,200 for family coverage, and with annual out-of-pocket expenses that do not exceed $5,600 or $11,200, respectively.