Mobile Web applications (a.k.a., Web apps) stand for an important trend for next-generation Internet-based software. Currently popular mobile Web apps need to be adapted to various and ever-changing contexts and personalized user requirements. Based on our over-decade research experiences and practice on the Internetware paradigm, this position article describes an Internetware-oriented approach to designing, developing, and deploying situational mobile Web apps, by synthesizing the resources and services of mobile and cloud. Guided by a novel Service-Model-View-Controller (SMVC) software model, a mobile Web app is organized into a well-defined structure that facilitates adaptation including online/offline data access, computation offloading, user interface optimization, hybrid composition, etc. We provide efficient runtime support spanning mobile and cloud to make mobile Web apps more flexibly adaptive. The proof-of-concept evaluation demonstrates that our approach can benefit end-users with optimized user experience of mobile Web apps.