I don't know the acronym JTIE, but I'll take a leap of faith and assume you mean either Joint Tenancy with Right of Survivorship or Tenancy by the Entirety.
As I am sure you know, the usual answer in inheritance from a spouse is that there is a step-up for the one half that was includible in the deceased spouse's estate. And yes, assuming you mean by "... including the depreciation.", that there is no longer any unrecaptured section 1250 gain as to the inherited half, yes, that is the case.
But you have posed a screwy set of facts. Did W ever actually have beneficial ownership of half of the property, and, if so, did she still have it when she died? Or did H "steal" her half of the property from W when they split? Or did W just leave and, effectively, abandon/give that half to H? Does section 1041 cause the transfer of W's half at the time she split to be treated as a gift?
Unless there are facts to show a particular scenario, I think it would be perfectly reasonable to claim the step-up for half. But I'd also be prepared for a challenge along the lines that H (beneficially) owned 100% all along, so no step-up applies.
And not that it's dispositive or even necessarily relevant, but what name or names were at the top of the Schedule E each year?