I have been working on the Berghaus family for quite some time and have never been able to make the jump "across the pond." We know the family from its days in southern Missouri: first, Newton county and then Billings in Christian county. But I do know that one of the sons was born in Cincinnati, so my guess is that the family was there very early, then went to Ferdinand, Indiana and then to Missouri.
When Bernard Heinrich Berghaus and his wife, Clara Schnier, lived in Ohio, he shows up on the census as "Barney Barkhouse." Does any of this ring a bell with you. Their Cincinnati stay was around 1860.