there's residency for immigration purposes (you are presumably non-resident aliens immigration-wise) and for tax purposes. if you are working under an H1B visa, I think you are considered a resident alien for tax purposes. anyway, as an NRA under an F1 student visa, I opened accounts with EmigrantDirect and MyBankingDirect, both of which now offer 4.0% APY.
FYI, as an NRA for tax purposes, bank interest (money markets, CDs) is tax exempt. ditto for obligations of the US government or its agencies - if I were to buy municipal bonds or a municipal bond fund, the dividends would be tax exempt (the capital gains on the bond fund would not be). however, NRAs can't own US savings bonds; you can buy the other treasury instruments from your bank or from TreasuryDIrect (the website), but they are a bit less practical for small investors. here's a summary of the rules for NRAs if it interests you:
http://invest-faq.com/articles/tax-non-us-nat.html
it sounds like you are resident aliens (for tax purposes), though, so you pay tax just like a US citizen. check with your banks again, sometimes they don't know the difference between residency for tax and for immigration. you should have absolutely no problems opening an account. you should also be able to open an account with most brokerages as well. I highly recommend opening a Roth IRA for your retirement; the earnings will be tax free when withdrawn (unless the tax code changes radically), and you'll only have your own country's taxes to deal with, unless you have migrated here by then.