Federal law doesnt prohibit discrimination on the basis of an employees or applicants marital status. If an employer flatly banned spouses from working at the same company, even if they had no interaction with each other at work, that could be discrimination based on marital status.
Can a married couple work together?
While some employers have policies against dating a co-worker or hiring a relative of an existing employee, most of the companies with policies simply restrict relatives from working in a direct reporting relationship. Working at the same level — or in a different department — as your spouse is generally fair game.
Why working with your spouse is a bad idea?
That all said, its a bad idea to work with your spouse when youre not able to separate your relationship and your work. You dont want to have to keep your relationship a secret, which can not only get you in trouble if youre caught, but can also cause tension in your relationship.