Hanzi has some underlining when dealing with foreign names, etc.
- What are the rules regarding Hanzi underlining?
edit: Would I underline 中国 in a text that includes underlining?
This page and it's Chinese version might help: Proper name mark - Wikipedia
By the way, we do not use underline as a punctuation in modern simplified Chinese writing. But in a passage (maybe classical Chinese texts) where underline is used, 中国 should be underlined according to the rules.
Actually, it is taught in Hong Kong and Taiwan, but rarely used in mainland China currently. During the early days of the Republic of China (ROC), a new set of punctuations was introduced in writing and printing. The traditional Chinese is written vertically and a straight line is drawn on the left side of proper noun. For those names of books, a wavy line is drawn instead. For horizontal writing, a line is drawn under a proper noun. Its function is similar to the capitalisation of proper nouns in English.