Translation:All happy families resemble one another.
So one happy family resembles another, or members of happy damilies look like their relatives?
I would assume the former, but in theory it could mean the latter as well.
This is (half) a quote from Leo Tolstoy's Anna Karenina, which PookaGar completed above:
"All happy families are alike; each unhappy family is unhappy in its own way."
Do you not need "på" after "å ligne"? Both translations are accepted, but I had always thought "å ligne" had to be "å ligne på"