I have h1-b status. I am about to file for a green card through my work that I have been working at for the last 2 years after finishing undergrads. If I were to get married before filing the green card, would my husband get green card the same time as me.
He just finished his master and is about to apply for OPT.

Also, can he change his status while we wait on the green card.

Please start your GC process even without your husband name i.e status - single (earlier the better).
Once you get I-140 Approval Notice please proceed further : i.e Mention your husband name while filing for "AOS" or "I-485"

Please consult with your company lawyer and get first hand info.

Marrying will not help at all...since the company is sponsoring ur greencard it only applies for u......after u get ur green card then only u can apply for ur husband which will take many more years.....so i dont think its worth to wait that long...better he find a job and try to find a h1b and possibly green card sponsor himself...... plus ur green card is also not in hand ...ur greencard will itself take so many years if EB3 category...so its a waste of time and energy

I have to disagree with jeffgordon11419. What no_more_crush said is right and I suggest you do as he suggested.

Unlike jeffgordon11419 said, even though your company is applying for you on employment basis, your spouse can still be included at the time of AOS(Adjustment of Status). Since you have undergrad degree and 2 years of experience you will qualify for EB3 which currently has back log of 3 years. So in worst case scenario your I-485 will be applied 3 years after you apply for labor.

My suggestion is to lay out your scenario to the immigration lawyer who will be handling your case so that you can get clear picture of the necessary steps in GC application.