In a nutshell:
1. I-751 needs to be filed within 90 days of GC expiration. Not earlier, not later.
2. You need to submit a lot of evidence of bonafide marriage to ensure you don't get RFE.
3. You send the packet with forms and evidence, wait for biometrics appointment (can be waived by USCIS).
4. You will receive I-797 aka extension letter which would extend validity of expired GC by 48 months. It can be used together with expired GC to travel or prove status
5. You then wait a long while to get any update. It could be RFE, interview (can be waived), or decision on I-751.
Also, if your husband's social security card says "Valid for work only with DHS authorization" - go to SSA office any time now, file SS-5 and get unrestricted SS card. This can be used with driver's license or state ID instead of GC for I-9 verification at work. Forget about showing GC to employers, it has major drawbacks.
I hope this helps and good luck!