We report second- and third-harmonic generation in monolayer MoS2 as a tool for imaging and accurately characterizing the material's nonlinear optical properties under 1560 nm excitation. Using a surface nonlinear optics treatment, we derive expressions relating experimental measurements to second- and third-order nonlinear sheet susceptibility magnitudes, obtaining values of $| {\chi }_{{\rm{s}}}^{(2)}| \ =2.0\times {10}^{-20}$ m2 V−1 and, for the first time for monolayer MoS2, $| {\chi }_{{\rm{s}}}^{(3)}| =1.7\times {10}^{-28}$ m3 V−2. These sheet susceptibilities correspond to effective bulk nonlinear susceptibility values of $| {\chi }_{{\rm{b}}}^{(2)}| =2.9\ \times {10}^{-11}$ m V−1 and $| {\chi }_{{\rm{b}}}^{(3)}| =2.4\times {10}^{-19}$ m2 V−2, accounting for the sheet thickness. Experimental comparisons between MoS2 and graphene are also performed, demonstrating ~3.4 times stronger third-order sheet nonlinearity in monolayer MoS2, highlighting the material's potential for nonlinear photonics in the telecommunications C band.