My family has a very good relationship with a Japanese family since many decades ago. When I was a kid, I used to play when their sons, and I visited them once and stayed at their home for a month. Now that we are adults, we use to talk on social media and they have visited us sometimes.

In my language, we can use the word "family" as a hyperbole to mean really close friends (as in "you're such a good friend that I consider you my family"). Also, I feel like they are an extension of my family, since the two have been connected many years.

Would it be polite if I refer them casually as "家族" or "日本の家族"? (As in "I have a family from my country, but you are my family from Japan"). For example, when captioning a picture in which we appear together.

Since the Japanese meaning of family might be different, I am worried that they may find it a weird choice of words, but it is what I would say in my language. I tried to search this before asking, but it is too specific.