If my husband dies before I do, do I have legal access to his bank account and or pension if we do not have joint accounts?
1) The pension is governed by its terms. Some pensions will pass to the spouse, some will not. She should discuss this with the pension administrator and check all pension-related documentation.
2) An asset of your husband's that is not joint will pass according to his will (if he has one) or by operation of law, or intestate succession, if he does not. Presumably it will pass to you (though you should verify this--he could will it to a child, relative, charity, etc.), but even if it does, it will have to go through the probate process, which could tie the assets up for some time. If having immediate access is a concern, he should either make it a joint account, or open up a separate joint account that will at least have enough money in it to tide you over for a while.
If it is not a joint account and you do not have a beneficiary designation on file then you will have to wait until you or someone is appointed as personal representative of his estate to access the funds.
As for his pension, it depends on the rules of the plan and again, if you are the beneficiary of the pension if it so permits.
You should cantact the bank and pension administrator to discuss these issues as well as an estate planner. They are not something to leave until the last minute. Good luck.