If a husband and wife have a joint account and each have a debit card, can the husband cancel both debit cards or can he only cancel his own?

It depends how your account t&c's read, but if it is joint "or" account, they have equal rights...he could come in a close the account, right? What would be the difference?

I would say to be very careful with this. Why does he want to cancel the wife's card? Bob is right, but I would still tread lightly. Bad PR is hard to overcome.

It would be similar to removing the wife's name without her consent.

If you're strictly speaking about the cards, it depends how you issue them, IMO. Do they each have their own 16 digit numbers, or do they have the same number? Most places offer each cardholder a different number so that in the case of loss or theft only one card has to be cancelled. In that case, then the husband could only cancel his own, and the wife hers, respectively.
If one of the two joint signers reports both cards as lost or stolen, I would hotcard them both, but only issue a new one to the person reporting (until I spoke to the other person on the account directly to make sure they wanted a new card).
Is that what you meant?

Be sure to look at your cardholder and/or deposit account agreements.