Now this sounds familiar! I'm related to the Chicago Nibbes. My Grandfather was Jerome Francis Nibbe (of Chicago, b. 1910), son of Frank Edward Nibbe (Chicago, b. 1885), son of Peter Nibbe (Chicago, b. 1860), son of Charles H Nibbe (who immigrated in 1848 to Chicago from Blankenese, Holstein -- near Hamburg). Charles H was born in 1827, and near as I can he fled the First Schleswig War on the ship Magdalene out of Bremen.
Charles H Nibbe married Eva Elisabeth Sharber (of Saxony; b. 1836; daughter of Christina Sparbach b. 1793 who eventually came to live with the Nibbes in Chicago; though it's possible that Christina might be Eva Elisabeth's grandmother), probably after he moved to Chicago as she wasn't on that ship out of Bremen. She's also 9 years his junior so she would have only been about 12 when Charles H. emigrated.
They had several children: Peter Nibbe (b. 1860), Elise Nibbe (b. 1863), Minnie Nibbe (b. 1868), Emma Sophia Nibbe (b. 1870 d. 1907), Paul Nibbe (b. 1873), Pauline Nibbe )b. 1877)
So, I'm pretty positive these are the Chicago Nibbes you are looking for.
It gets a big confusing when Charles H came over as he used several different spellings of his name: Nibbe, Neibe, Neebe, Neepe. Nibbe is used the most consistently and importantly he used it when he applied for a passport in 1871 when he listed his origin as Blankenese, Holstein and exact date of birth.
Family oral tradition is that he was fleeing impressment into Bismark's army. Maybe he didn't want to be found!
Charles H Nibbe and Eva Elisabeth Sharber's son Peter Nibbe (b. 1860) married Anna (Nibbe; b. 1860). They also had many children: Carrie H Nibbe (b. 1880), Rosa T Nibbe (b. 1881), Charles Nibbe (b. 1884), Frank Edward Nibbe (b. 1885), Catherine Nibbe (b. 1887), Elizabeth Nibbe (b. 1889), Marie Nibbe (b. 1900)
Looking forward to hearing from you!