I'm confused by the time line on this. Is this referring to one particular Thursday, because it says "В четверг" and not "По четвергам"? Then the tense of the verb "спит" seems confusing to me. I was thinking this meant something like "On Thursday morning my husband will be asleep"
Doesn't have to be the current date or time, no... You can say "On Thursday morning" to mean the coming Thursday morning, even if that date is still in the future. This is certainly valid for English, but I'm not 100% sure that that's what the Russian sentence is trying to say, although I think it is.
And you should be confused, because the English is so ambiguous and uncertain.
If it's a regular event, then it should be "On Thursday morningS my husband sleeps [late, in]."
If it refers to a particular Thursday, then the verb should be past or future tense, not present tense, with "last/next Thursday" implied by the verb.
In the bare-bones structure of the exercise, it leaves one dangling, and doesn't actually make much sense.
Yes, these exercises concerning day of the week are horribly confusing and inconsistent concerning the single monday vs multiple mondays distinction. I would expect the former to always align with в+accusative, and the latter with по+dative, but this isn't always the case with duolingo.