Short Answer: 'YES', definitely, they do ...
When you "Register" to become a User/Patron of ANY Part of 'FamilySearch', you ARE 'Officially' registering as an INDIVIDUAL; and, NOT, as a 'Couple' (or, 'Group' of people).
EACH member of one's Family NEEDS their OWN separate 'FamilySearch' Account, even Children (when they are of age).
For example ...
In "Family Tree" of 'FamilySearch', EVERY User/Patron gets a "Private Space" for THEIR "Living" individuals/persons, that they add to "Family Tree" of 'FamilySearch'.
That said ...
'Yes', a Husband and a Wife NEED their OWN separate 'FamilySearch' Account; and, so do each of their Children (when they are of age).
I hope this helps.
Having a separate account does give benefits. I work both in my and my husband's side of the family tree. On my account I added him and his living parents then linked them to his deceased grandparents so I can see and work on his line but I do not get many hints or reminders which can be fun to see and valuable when researching. So he does have his own account and sometimes I log in as him and I see different things in what pictures are shared on his line(that landing FS home page) and the list of hints and even temple suggestions is different because they draw from his line not mine. So it is best to have separate accounts but you can certainly build and work on your spouse tree from your account.