What does the EOE Act say about spouces working together?

The husband should be paid more but the wife gets to spend more of it?

Nothing

I meant spouse.

Absolutely nothing. It is up to the employer whether they want to permit spouses to work together. The EEO legislation simply addresses discrimination on the basis of protected classes, and the federal EEO does not include marital status as a protected class (although some states do). Even in the states that state that marital status is a protected class, there is no encouragement or prohibition of spouses working together.

For sexual harassment reasons, and the avoidance of possible future claims, most employers will prohibit spouses or people who are dating from working in the same chain of command… ie, one cannot have a position of authority over the other. Again, it is not illegal to allow that, but it is risky if the relationship goes sour and one of the partners later alleges being treated adversely based on the break-up.