Am I HSA qualified if I am covered on two health plans, one of which is not high deductible?

You are probably not eligible for an HSA based on your secondary coverage.

From IRS Pub 969 (emphasis added):

Qualifying for an HSA

To be an eligible individual and qualify for an HSA, you must meet the following requirements:

• You are covered under a high deductible health plan (HDHP), described later, on the first day of the month.
• You have no other health coverage except what is permitted under Other health coverage, later.
• You aren’t enrolled in Medicare.
• You can’t be claimed as a dependent on someone else’s 2019 tax return.

If you meet these requirements, you are an eligible individual even if your spouse has non-HDHP family coverage, provided your spouse’s coverage doesn’t cover you.

Pub 969 also lists some specific exemptions to this rule about what kinds of "secondary coverage" you can have, but being covered by someone else's health insurance seems to be a pretty straightforward violation of the eligibility rules.