us citizen applying for husband with h1 visa

[ally]

I am a US citizen and my husband is on h1 visa. We still have to file for his green card. He is still working with the company that sponsered his h1.
Would it be safer for him to leave the company as we are married even though I havent applied for his paperwork yet?
Would it jeopardize his legal status as his company work permit will be cancelled as soon as he resigns?

Please help