The phrase 'likeness between' is correct and can be used in written English.
You could use it to describe the similarities between two things. For example: "Despite their differences, there was a strong likeness between the two cultures."
Theophrastus says that Alcmaeon did not explain sensation by the principle of like to like (i.e., by the likeness between the sense organ and what is perceived), a principle which was used by many early Greek thinkers (e.g., Empedocles).
And the 20-year-old's question for Turner: "How have you got through life looking like me?" "Yeah, that is odd!" laughs the musician of the uncanny likeness between him and the young actor.
Friends exclaim at the likeness between them.
Is there a family likeness between this collection and its predecessors?
As he riffles tenderly through photographs of her, I am struck by the likeness between them.
There was also the strange and not accidental likeness between modern art and traditional comic art.
She said there were strong likenesses between her character and a more recent British royal beauty: Diana, Princess of Wales.
He searches out likenesses between Dutch classics and Persian poets, as if to establish secret corridors between separate worlds.
It mistakenly presumes that any kind of change will do.Mr Cameron's team can point to some superficial likenesses between their man and Mr Obama.
"Likenesses between William Randolph Hearst and Napoleon, Charlemagne, the Louis of France and the Popes of Rome are noted in Mr. Hearst's official biography," a reviewer remarked about Older's book, "yet it is possible that Mrs. Fremont Older, the biographer, is amazed at her own moderation".
The art of digression reached breathless heights in Samuel Butler's 1890 essay "Ramblings in Cheapside," which traverses turtle shells, the relation of eater to eaten, likenesses between common tradesmen and famous portraits, the worthlessness of most classical literature, the politics of parrots and the practical wisdom of slugs.
