Please clarify your question

Basically no, first if this is in the US there is no national data base on being married,

If you have such mistrust, I would say why do you not believe him?

Or even why does it matter ?

For free, no. But if you are willing to pay a fee you can look him up on one of those public records sites like Intellius. It would show marriage or divorce records. It would only show information about children if they were older and he had cosigned on a loan for them, for example.