Hi Christy3 & welcome
It's good that he and his wife didn't part on bitter terms, but I can understand, as his current partner of one year, that you wouldn't want this past relationship to be constantly paraded before you.
Were there children involved?
Who / what is in the photos that she sends & that he exhibits?
Are the cards sent for Christmas & birthdays?
Does he display them for longer than the usual period?
Does he see his ex-wife, or just get letters & cards ~ presumably containing notes from her??
I'm wondering ~ could it be that he wants to prove to you that his current relationship with her is simply one of innocent friendship, and that he has nothing to hide from you?