Travel with official passport & green card

[simpsons]

Hi,

I am an India citizen and I hold a Green Card. There is a cultural program in Mexico which I will be a part of and the govt of India has applied for an official passport(white cover) and Mexican visa on my behalf. I will have to deposit my original passport and travel only using the official passport.

I wanted to know if I will be able to enter and exit the US with the official passport and my green card alone?

Any advise in this matter will be highly appreciated.