There is a lot of unbiblical, awful advice answering this thread.
Hasn't anyone read that one saved person in a marriage sanctifies the union?
The Apostle Paul wrote it, look it up!
Do you think it would be better for the children to live in a one parent home?
Don't you think God can use the Christ like example of this believer to
soften her common law husband's heart? - God does it all the time.
Now if there is a question of battery or unfaithfulness that is one thing,
but to tell someone to leave their common law husband, who they share a child with,
because he isn't saved is just AWFUL!