Well, I am afraid the definition of a house (free standing one) in English means "别墅”in Chinese. You have to understand that in China, we call any kind of property a 房子. They can be a cottage, a unit, an apartment, a villa, a duplex , a townhouse or a freestanding house. In the cities, the mojority can only afford for a unit. So it is so likely that he/she means to buy a unit when talking about " 买房子" . That is kind a culture shock, isn't it? :)

中文裡頭的 "家" 有兩種意思 可以指 1 眷屬共同生活的場所 即建築物 或說 房子 住宅 集合住宅 公寓 等等 也可以指 2 一門之內共同生活 或 一門之內共同生活的人 而英文的 house 應該與第一義相近 至於第二義 則比較接近英文的 home 我們習慣說 買賣房子 或 住宅交易 或 搬家 等等 但是 我們不說 買賣一個家 搬家一詞 還是著重在 人的遷移 指 共同生活的一群人遷居到別處 而家具的搬移只是一種附屬的行為

Yes, it's correct. But "house" can also mean “全家人---- all the people living in a house” or " 某种用途的建筑物----- a building used for a particular purpose” according to different contexts.