I have received a marvellously nasty Christmas card from my sister-in-law. Absolutely dripping saccharine venom.
Now normally I wouldn't dream of passing shit like this around. I might take a sanity-check with someone close to me whom she'll never meet, but in general I wouldn't show private correspondence around.
I also feel strongly one shouldn't mess with loyalty between husband and wife.
Buuuuuut... she's signed my DB's name to her shit. 
DB is usually the one who writes the cards to me, or at the very least they both sign them. There's nothing to show he's even seen this one.
My options are
a) I can ignore and have my DB wondering why people are apparently behaving weirdly.
b) I can speak to her directly – my normal approach, but in my old age I've learned that engaging with batshit just elicits... more batshit.
c) I can send him a copy of the card she has written and to which she has appended both his and her names.
Now it may or not be an actual good move to send him a copy: still pondering that one! But in terms of whether it's ethically permissable:
YABU: it's a private note from her to you, he's not entitled to know the contents and what's more you should be at pains never to play husband off against wife;
YANBU: it's a note with his name at the bottom, he's entitled to know what's being said in his name.