Semiconductor heterostructures are fundamental building blocks for many important device applications. The emergence of two-dimensional semiconductors opens up a new realm for creating heterostructures. As the bandgaps of transition metal dichalcogenides thin films have sensitive layer dependence, it is natural to create lateral heterojunctions using the same materials with different thicknesses. Using scanning tunneling microscopy and spectroscopy, here we show the real space image of electronic structures across the bilayer-monolayer interface in MoSe2 and WSe2. Most bilayer-monolayer heterojunctions are found to have a zigzag-orientated interface, and the band alignment of such atomically sharp heterojunctions is of type-I with a well-defined interface mode which acts as a narrower-gap quantum wire. The ability to utilize such commonly existing thickness terrace as lateral heterojunctions is a crucial addition to the tool set for device applications based on atomically thin transition metal dichalcogenides, with the advantage of easy and flexible implementation.