What does the Kabbalah (or Zohar) say are the characteristics of a besheret?

Answer

In Kaballa it is explained that man and his wife are connected via their soul, as branches to trees. Esoterically, the roots of their souls interact as such; their characteristics being from the same Neshama source - (source: "Sha'arei Kedusha" 3:5; quoting his teacher "Ari Zal;" "Torah Lishmo" by Ben Ish Chai, 506).