Should I tell my husband I might not believe in God?

Yes you should tell him how you feel, and more importantly it is okay to have doubts. You could even say that it's healthy in a way. I had doubts and questions too, even after growing up attending a private church-based school. Later in life I began attending a church that was a lot different than what I had grown up with. It was less formal, less ceremonial and more relaxed. They offered a cl where you could come and learn the ABCs of Christianity and no question was off limits. It was OK to be a doubter and they encouraged you to ask and read and study and attend cl and participate, etc. At the end maybe not every question was answered but the result was that the seeking of the answers made my faith stronger than ever. It's a never ending learning process. We are not meant to understand everything....that's what makes us human and God God.