first of all we don't want to mislead you - we are NOT experts in residence permit or EU law regarding family members right to stay in Denmark.
So we strongly recommend you to seek advice (also) with other authorities or your A-kasse before make any judgements about this.
We think a little mistake can be crusial for you and your husband.
However you can get our opinion on your situation:
As we read in the law you have the right to stay with you husband if you are married to a EU-citizen and he has permit to work and stay in Denmark (he always has..). This is according to EU-opholdsbekendtgørelsen §8.
A non-EU spouse, children and grandchildren acquire the right of permanent residence if they have lived legally in the host country for a period of 5 continuous years.
They can then stay as long as they want even if they don't work and need income support. They should enjoy the same rights, benefits and advantages as nationals.
And if that's the case then you also have the right to work fulltime here in Denmark after you graduate. And therefor also the right to get Unemployment benefits.
You can read more about the EU-rules here:
If you seek (Permanent) residence card:
After the 5 years period you will usually get the permanent residense permit. Read here:
In your question you talk about different ways to get residence permit in Denmark:
Establishment Card, Green Card (Green Card Scheme don't exists anymore), and Family reunification.
These ways to get residence permit is for non-EU Nationals who is not married to a EU-citizen.
But regardsless of this: You are right about that you can not get Establishment Card, if you receives Unemployment benefits as an graduate.
However the same is not the case with Family reunification. You can apply for and get Family reunification regardless of you receiving Unemployment benefits.
Remember to get this verified before make any judgements. Bot we hope it has clarified something for you.