You're misunderstanding how these work.
Scenario A: 401k
You contribute the max to your 401k. The money is deducted, pre-tax, from your paychecks throughout the year. At the end of the year, you get a W-2, and the wages box will not include that amount, thus reducing your AGI, and you'd have 2 401ks (one for each of you).
Scenario B: Traditional IRA
You don't contribute to your 401k at work. Instead, you open a Traditional IRA account and put in the max amount. When you file your tax return, you'll deduct your contributions from your income, thus arriving at your AGI. Both of you would need your own IRA.
Really, the only reason to go with a traditional IRA over a 401k in your case would be investment options. Depending on what options are available through work, you might be fine with the 401k, and it would probably be easier.