[The following is irrelevant since her spouse has approved I-140 in hand already. Congratulations!]
I did some research for the H-4 visa EAD application process. According to USCIS, this category is ONLY available to an H-4 visa holder (you, in this case) if:
1) If you are the H-4 dependent spouse of an H-1B nonimmigrant; and
2) if your H-1B nonimmigrant spouse is the principal beneficiary of an approved Form I-140, Immigrant Petition for Alien Worker; or has been granted H-1B status under sections 106(a) and (b) of the AC21. Under AC21, H-1B nonimmigrants seeking employment-based lawful permanent residence may be eligible to work and remain in the United States beyond the six-year H-1B period of admission limitation.
To put it into plain English, your spouse MUST be applying for employment-based Green Card and his application has been approved. (A21 would not apply since you will need working permit before your spouse hits the six-year limit for H-1B)
That is not a slam dunk unless your spouse qualifies for Extraordinary Ability category within two years. (Assuming your spouse does not have an advanced degree now and is not an multinational executive/manager.)