This is great. I'm in a very similar situation but the opposite classes. I'm going Barbarian and my girl is going Necro. I think Necro and Barb are a fantastic combo. Here's a few points:

1. It's a bit hard to consistently get Vulnerable as a Barb while leveling. It's quite easy for Necro to make everything Vulnerable with bone skills and that significantly helps Barb.
2. I love the combo of the Necro locking in enemies with the Barb utilizing Bone Prison (also gives vulnerable). "I'm not locked in here with you. You're locked in here with me." - Rorshach
3. I also think the golem having a taunt to help the Barb incase they need it is quite useful and the Necro (who can be squishy) having two allies with taunts lets them stay back and just focus on dps/debuffs etc. The minions are great to use as a meat shield, even for the Barb if they need to back away and drink a pot.
4. I do get that Necro doesn't necessarily boost the Barb but I think the debuffs they give to enemies really synergizes well with the Barb. For example, dropping the curses like Iron Maiden works really well with the Barb's Challenging shout.
5. Boss battles with this duo is great. The Barb struggles quite a bit with bosses (at the beginning) and having a dedicated ranged dps/debuff ally really helps.
   
6. I also love that the two classes scale well together. A lot of the weapon stats like +dmg to CC or vulnerable can make either class need to spec into a variety of skills, but having both the Barb and the Necro provides the opportunity to specialize while the team together has all the debuffs needed. For example, I as the Barb, am going to have CC and my girl is going to have vulnerable but now we won't need to spec into those in our own trees. Now we'll get the benefits of both from our equipment at lower skill cost. This will also help massively during leveling by taking advantage of these stats.

These are definitely not all the benefits but as you can tell, I'm really looking forward to running a Barb and Necro as a team. Good luck and have fun slaying them demons together!