I hope you don't mind if I answer your question in English, I can type faster this way:
Let me start with how engineers classuify "Bridges". Actually there are 2 types of bridges - "Bridge Overpass" and "Bridge Underpass". Both are considered as "Grade Separation".
Overpass - You have an existing roadway and you need to build a bridge to fly over and across the existing roadway. Therefore, you need to build bridge bents (橋墩) to "fly over" the existing roadway (e.g. 加士居道天橋)。
Underpass - You have an existing roadway and you have physical limitations and do not want to "fly over", then you have another option, which is trenching underneath the existing roadway and build an underpass to cross the existing road surface. But you will end up having the existing roadway supported by a bridge at grade and the new roadway is depressed to go under.
So, to answer your question: are all bridges need to be above see level or existing road surface? The answer is no, not necessary.
When you take a side view of a bridge (such as Ching Ma Bridge), you may notice that the profile of the bridge is slightly concave up - center portion is higher than the two bridge approaches. There are many reasons for it, such as drainage, load calculations, aesthetics etc.
I hope I touched the topics that you are interested, if not, feel free to ask again.
圖片參考:
http://hk.yimg.com/i/icon/16/1.gif