What about her permission?
That sounds fair enough, but following that logic surely her permission was also needed for the bundling to go ahead. If she gave permission, she has no case as she presumably would have notionally acknowledged having "read the small print" that this is what would happen. If their terms didn't make it adequately clear that both bills would come in the same envelope, then she has a case.
If it's the case that none of these points are very clear, another interesting question raises its head: What degree of privacy are spouses, legally, entitled to *from each other*? I only ask because there are many other aspects of law where being married to each other makes a difference, e.g. (if I can believe Law & Order) you cannot be compelled to testify in court against your spouse. That seems to be a case where the law treats a marital unit as, forgive the phrasing, a law unto itself - could this be another?
PS @the sadly numerous misogynistic rants posted above: Christ, get some perspective. Mating for life is a relatively new notion for us as a species and some people just aren't cut out for it. You lot are awfully keen to make horrible pronouncements about a situation you know sod-all about. Grow up please.