White fish is a play on the phrase "wife-ish". (say them both really fast) When you are in a committed relationship with a girl, engaged to her, living together, raising a family together, etc. She is pretty much your wife in every way except there is no legal paperwork.
sounds better than wife
---ish because the ish makes it seem like there is a lack of commitment.
They have lived together for 20 years, have two kids, and three grand babies, but just have not taken to time go to the courthouse. She is his White Fish.
The soldier got deployed before they could make it down the isle. Guys in his battalion see his pictures and ask who the hottie is, he says "That's my White Fish".