If you invest in index funds (whether they are stock indexes or bond indexes) they are about as diversified as you can get. That is the nature of an index fund - it has literally hundreds, if not thousands of traded companies in their holdings. Index investing tracks the basic market, so you'll never make the crazy highs that some non-index funds might shoot upwards to, but you'll also never have them fail and take every dime you invested with it.
For instance, VTSAX tracks the CRSP Total Market Index, which is nearly 4,000 constituents across mega, large, small and micro capitalizations, representing nearly 100% of the U.S. investable equity market.
And the big thing about index funds are they are self cleansing. If a company fails, it drops out of the index fund's holdings and is replaced with an up and coming company. Index funds will fluctuate with the market ups and downs, but the chances of and index fund itself (like any of Vanguard's offerings) failing completely is so far outside of the chance of happening as to be virtually impossible. Okay, sure, it could happen, but only in a case where the entire stock market melts down and in the event of that occurring, you'll have bigger issues to worry about than what happened to your investments.
If you are married, you should consider your and your spouse's investments as a collective. A couple of IRAs, maybe 2-4 work related accounts like 401Ks or 403Bs... but they are parts of a whole. You have a portfolio made up of several buckets, but they'll all get poured into the same place, so you place the funds you like into them with an eye towards meeting your total asset allocation in the most efficient way.
As it does sound like you're missing some of the basic points of how to invest and what investments are and how the market actually works, I'd suggest you read Jim Collins' stock series (free to read through at the link), or check out his book (based on his website) "The Simple Path To Wealth" available here:
http://jlcollinsnh.com/stock-series/You should be able to understand the following after reading all of that.
Next, you'd write an
investment policy statement. This is your guidelines for what to do and how you will do it.
With your IPS written, you then figure out what asset allocation you are comfortable with. If it is as simple as a 70% stock, 30% bond, then you set that up across ALL of your accounts - IRAs, 401Ks, taxable accounts - but do so in to manage the funds so they are in the accounts that are tax-efficient for the fund placement. So hold the bond index funds inside the tax advantaged accounts like a IRA or 401K, and fill up any other space in the accounts that are left with your stock index funds. Since they tend to operate the most tax efficiently, it doesn't matter as much which account they go in.
https://www.bogleheads.org/wiki/Asset_allocationhttps://www.bogleheads.org/wiki/Tax-efficient_fund_placementYou don't have to do a 70/30 split in each account, and you don't have to hold completely different funds in each account. If you want to be an index investor and like two funds, like say Vanguard's VTSAX for stocks and VBTLX for bonds, you can hold just those two across all your accounts to equal your asset allocation. Again, as they are index funds, you are in no real danger of them disappearing or failing. It sounds simple, and that's how it should be, but lots of advisers out there create complicated 20-40 (or more) fund portfolios to make it look like they are super intelligent and investing is too complicated and scary. And that is the purpose - to scare the crap out of Average Joe - how can investing be so simple if the guy I was using had me in 24 funds? I can't invest in just 2 (3,4) funds and be safe - that can't be right! (but it is!)
I hold a 3 fund (index) portfolio across 7 different accounts. I have the bonds in the tax advantaged accounts like an IRA or 401k. The exact amounts of how much of each fund are in what accounts is not remotely important; what is important is that I filled my asset allocation in the most tax efficient manner possible.
That sounds sort of confusing typing it out, but I do think if you read the links provided (and of course ask more questions if you run into anything) you'll get it figured out pretty fast. The Collins series is instrumental to understanding how it all works together, and it's a great read to boot.