I owned the book as a child in the mid- to late-fifties. The size of the book may have been larger than typical for a children’s book. Each chapter told a story of one of the fictional families who lived on a block. As I recall, they were linked by the relationships and adventures of the children. I remember being intensely curious about how other people lived.
This sounds like 365 Bedtime Stories by Nan Gilbert, described in the most requested books section on this site. The families live on What-a-Jolly Street.