"Her husband is Chinese."
actually她丈夫是中國人should be fine
--A native cantonese speaker trying out duolingo the first time
Yes, for personal relationships 的 can be omitted. However, using 的 is still correct.
Pedagogically, I agree that Duolingo should discourage the omission of 的 before personal relationships. For a beginning student, teaching this (completely voluntary) exception to the grammar rules would unnecessarily confuse them when they haven't mastered the rule in the first place.
However, for those taking placement/proficiency tests, 的 omissions should be allowed.
Our Chinese teacher told us this rule as the second thing she taught us, and we (university students) didn't have any problem with that. We're not native English speakers, though, and Duolingo can't explain us the grammar rules.
I'm a begginer who was also taught this rule... I have unnecessary failed twice now because I'm too used to omit it in these cases, which is very unfair