I think I would seek the answer to your question following a different logical approach.
I'd ask: "Is there is such thing as friendship between a male and a female dog?" or "...a male and a female cat?" or "a bull and a cow" or "...a ram and an ewe?"
In most cases, when you examine such a relationship amid animals and apply the similarity of their approach to each other to the approach humans have, you will conclude that "... no, there's not! "; their natural mating desire after a lengthy exposure to each others presence always overcomes the 'propriety protocol' that behavior between friends shall always comply to and the two always end up tied up and bound in an emotional mess which may also complicate and destroy their relationship to each one's social circle.
And the main reason for this trouble is the intensity of the instinct of the mating desire which becomes hard to controll, even for the most properly educated individuals.
Usually girlies call a guy "he's my friend" when they are incapable to decide between 3-4 to be lovers who flirt them. And then for some, later on in life, when their personal dignity has been totally humiliated and they have been switching love partners in the fashion somoeone may switch trousers, calling a man 'a friend' is a cheap excuse for their loose moral condition.
There's no chance you can have a better friend of the opposite gender than your sole partner once you are engaged in a healthy relationship; the rest are called "a friend of us" instead of "my friend" or simply "acquaintances". The other way leads only to emotional chaos which in mid term corrupts an entire society. And do me a favor, please, get yourself a pair of longer, wider trousers, try to reflect the true superiority that a human shall have to a dog!