The emergence of two-dimensional electronic materials has stimulated proposals of novel electronic and photonic devices based on the heterostructures of transition metal dichalcogenides. Here we report the determination of band offsets in the heterostructures of transition metal dichalcogenides by using microbeam X-ray photoelectron spectroscopy and scanning tunnelling microscopy/spectroscopy. We determine a type-II alignment between MoS2 and WSe2 with a valence band offset value of 0.83 eV and a conduction band offset of 0.76 eV. First-principles calculations show that in this heterostructure with dissimilar chalcogen atoms, the electronic structures of WSe2 and MoS2 are well retained in their respective layers due to a weak interlayer coupling. Moreover, a valence band offset of 0.94 eV is obtained from density functional theory, consistent with the experimental determination.