Is marriage certificate mandatory for H1B visa extension.

Hi, my spouse holds H1B, which is valid till Dec- 2014. We got married in Feb 2014. After marriage, he travelled to USA alone as my Passport is under renewal process, I got my new passport with my name with Wife of my spouse name.

At the time of my H4 interview I have provided marriage certificate provided by Church authority (Christian marriage).
I travelled to USA alone with out gov registered marriage certificate.

Is it mandatory to submit registered marriage certificate for H1B and H4 visa extension or can we manage with the marriage certificate provided by our Church Authority?

Can we travel to India once we start our visa renewal process?

Please help us in answering our queries.

Thanks in advance