H1B re-entry docs

Hi,
I wanted to check exactly what documents Canadians holding H1B and H4 require when re-entering the US. We have not left the US since receiving our H1B and H4 in Oct. We are going to Europe and my husband and I a coming back to the US at different times.
From what I understand my husband (H1B holder) needs his I-797, past 2 pay stubs and a letter from his employer saying he is an employee there. Does he need to bring things like copies of his degrees or the actual degrees?
When I re-enter (on H4) need my I-797, a copy of my husbands I-797, a copy of his passport, marriage certificate, his pay stubs and a letter from his employer.
Are we missing anything?
Thank you!

For re-entry on H1, a copy of the last paystub is sufficent, along with a copy of the I-797 (or the info stub stapled in passport). There is no readjudication of his H1 at the POE.

For re-entry on H4, I-94 or I-797 will be sufficient. No need for any proof of marriage. That is overkill.

Clear, concise, and unequivocal answers to the officers questions are more important than carrying mounds of documents.