Hi Jennifer
There is a birth for an Albert MILLS registered in Dec Qtr 1865 in Ulverston Registration District Vol 8e Page 579. Ulverston covered Barrow-in-Furness at the time. Miles could easily be mistranscribed as Mills on its way to the GRO index.
The 1871 census has a family in Dalton, Barrow that has been transcribed as MIBER, and head of family Jane. A check of the image shows it could be MILES and the head, who is male, could be James. There are also 2 births of Miles children in Ulverston Reg District that match 2 of the children in the MIBER family, Alfred and Hannah.
Andy