I'm married filing jointly. If my spouse, children and self were covered under HDHP offered through my employer, do I say that my spouse was enrolled in a HDHP in 2016?

[ChrisV]

Yes, as long as your spouse was covered for the entire year through your HDHP, you would indicate that she was enrolled in one in 2016.

[B_Tax]

I have the same question, but need more details.
How do I answer the TurboTax question: "What type of High Deductible Health Plan did [my spouse] have on Dec. 1, 2018?  o Family, o Self only, o None"

If I have HDHP through my employer and my spouse is covered under that plan, does my spouse "have" a family plan OR does my spouse have "none" since technically I am the owner of the HDHP?

[Critter-3]

Although she is covered by your HDHP  she herself doesn't have a HDHP at her job ... say NONE. 

[B_Tax]

Thank you, Critter-3! 😊

[BillM223]

Technically, your spouse has Family coverage, however, the way the dialogue is done leads you to enter the wrong answer.

Your spouse did not have an HSA. Therefore, your spouse never went through her part of the HSA interview. Therefore, your spouse never indicated that she had HDHP coverage in 2019 (you did when you did your part of the HSA interview).

So as far as TurboTax knows, your spouse had no coverage for 2019.

However, when you answer "Family" or "Self" for 2018, then TurboTax incorrectly thinks that your spouse had coverage for 2018 but no coverage for 2019 (because it never asked her about 2019).

This confusion leads TurboTax to present a "lapse in coverage" message, even though you entered the right data.

So do what Critter-3 said and enter None, because this question actually only applies to taxpayers who (1) had an HSA in 2018, and (2) made contributions to it in 2018.

Every other taxpayer - no matter what coverage they had - should answer None.