Currently using... we both are using BoA savings, checking accounts and credit and debit cards. Just because... BoA is nearest to us. Haha. Any good recommendations?
Not them.

At least, not after you leave.
Here’s the “ideal” bank or credit union account:
1. No minimum balance requirement.
2. Low or no fees, including especially no debit/ATM card foreign transaction fee or incoming wire fee.
3. Free Bill Pay (so you can pay somebody in the U.S. in a pinch if you need to).
4. Doesn’t mind foreign addresses and F-1/F-2 visa holders.
5. Online and mobile friendly, e.g. it’d be nice to be able to deposit the oddball U.S. paper check using your smartphone.
I think I’m going to suggest Alliant Credit Union, which hits all these marks. That’s the credit union serving United Airlines employees, and others. (There are a few United employees in Singapore, so a Singapore mailing address isn’t a big deal — although like most institutions you have to opt for electronic statements to avoid a paper statement fee.) It costs US$10 to join (donation to a charity) if you don’t otherwise qualify for membership, and that’s it for life. Their High-Interest Checking Account pays decent interest on balances, and their ATM card is almost as globally fabulous as Schwab’s. (Instead of unlimited ATM operator fee rebates it’s US$20 maximum per month. And there’s no foreign currency markup — just the Visa network’s 1% charge.) They also offer a savings account which pays excellent interest, and if you don’t think you’ll ever use the Bill Pay feature or use an ATM that levies an operator fee then that’s enough. (Savings accounts are limited to 6 withdrawals per month, but cash withdrawn at an ATM doesn’t count.) You can have both, of course.
Like other institutions they have inactive and dormant account rules, so just make sure you understand those rules. A 50 cent steamed bun purchase using your chip-based Visa debit card is entirely sufficient for recording activity on the account and resetting the inactivity clock. So is ACH transferring a penny to or from your Schwab account.
There’s no tax on the interest if you’re a non-U.S. person outside the U.S. (or in some cases inside — F-1/F-2, I believe). Just file your W-8BEN, and you’re all set. You should be able to have separate or joint accounts, as you prefer. With separate accounts you should be able to set up reciprocal PoD arrangements. Or one of you can have savings, the other checking, both with PoDs to the other. As you prefer.
I suggest looking through DepositAccounts.com to find other candidates, but I think that one is a very good one, a “keeper” (along with a Schwab One account).