We’ve been seeing each other for three months.

The contraction combines the words we have.  In this sentence, seeing each other refers to a man and a woman courting, ‘going out’, or dating.  It does not mean that a person is ‘looking at’ another person.

我們二人約會，已有三個月了。

see, hear, find 之類的動詞，很少以「進行式」的面貌出現。然而，本句的動詞卻屬於「現在完成進行式」，除了配合表達「三個月之久」的含義外，更重要的是，本句動詞並非「(肉眼)看見」，而是「(男女)約會、出遊」的意思。