If our friend wants my husband and I to be on the board of their church, will we be financially responsible if the church fails?

Typically the governing documents of a non-profit include promises to hold board members harmless and defend them if anyone makes a claim on account of a member's actions. Usually this promise is funded by an insurance policy. You should look for such a promise and such a policy. Even if the promise and policy do not exist, board members generally have no personal responsibility memrely because they are board members for debts of the organization. However, as a board member you owe a duties of honesty, loyalty and good faith to the organization and if you breach those duties you may be sued, depending.