This is kind of irregular. It is a form from the bible but nowadays it is used only in very specific words.
More than that if someone says Labayit instead he doesn't sound very smart.
The XXah (connected to the end of the word as in habaitAH) is a post-position meaning towards. This sort of construction exists in many languages. You must have encountered it in Turkish for instance.
The ה at the end of the word is called "directional hey" and is quite common in the Bible. Apperently it is not used in modern hebrew except for specific expressions. There are other uses for ה as suffix in the Bible - it can cange the sense of a a word (add emphasis to it for example).