Ma biche is used to address your wife or girlfriend (even if it is not so common as eg mon trésor, ma chérie, and a bit humorous, as it is known as a funny catchphrase in a series of comedies of the 60s with Louis De Funès).
A woman may also address a dear female friend as ma biche. A man addressing a male friend as ma biche can be heard, but it is then very clearly on a bantering tone.

Ca va, ma biche ?

Bonjour, ma biche !

Biche, oh ma biche, lorsque tu soulignes au crayon noir tes jolis yeux… (famous song of the 60s)

But it would be rather unusual to use ma biche to refer to her if you are talking to another person (as in eg "Je viendrai avec ma biche", that would be a bit weird). I think it could even be perceived as demeaning or "macho", as une biche is also used in slang to refer to a sexy girl, a bit like fox in English (as in eg "tu as vu la nouvelle voisine ? Quelle jolie biche !"), or even to a woman interested in money. It is then much more usual to use some other tender terms as in:

je viendrai avec ma chérie

je viendrai avec ma chère et tendre

I don’t know about Canada and other French speaking parts of the world, but in France and Belgium “ma biche” sounds like the most old fashioned thing to say to someone. Better still, it was already so in the 1960s in the Gendarme films mentioned by Greg where that line was intended as comical, Louis de Funès’s character being an older generation chap with outdated manners.

You wouldn’t say “ma biche” to your partner seriously these days, even less refer to her that way when talking to someone else.

I am from Canada, Québec, and if you call a women “ma biche” you could get slapped. It is very close to “ma bitch”. Sometimes the “bitch” English word is used here and describes exactly the same thing when used in a French sentence (this is not correct, but we do borrow words from English, as we are surrounded by them).

Biche is also a female deer, so my girlfriend would not be happy with the reference. As others have pointed out, it is old fashionned and I never hear that around me.