There is mounting evidence for the coevolution of galaxies and their embedded massive black holes (MBHs) in a hierarchical structure formation paradigm. To tackle the nonlinear processes of galaxy-MBH interaction, we describe a self-consistent numerical framework which incorporates both galaxies and MBHs. The high-resolution adaptive mesh refinement (AMR) code Enzo is modified to model the formation and feedback of molecular clouds at their characteristic scale of 15.2 pc and the accretion of gas onto a MBH. Two major channels of MBH feedback, radiative feedback (X-ray photons followed through full 3D adaptive ray tracing) and mechanical feedback (bipolar jets resolved in high-resolution AMR), are employed. We investigate the coevolution of a 9.2e11 Msun galactic halo and its 1e5 Msun embedded MBH at redshift 3 in a cosmological LCDM simulation. The MBH feedback heats the surrounding ISM up to 1e6 K through photoionization and Compton heating and locally suppresses star formation in the galactic inner core. The feedback considerably changes the stellar distribution there. This new channel of feedback from a slowly growing MBH is particularly interesting because it is only locally dominant, and does not require the heating of gas globally on the disk. The MBH also self-regulates its growth by keeping the surrounding ISM hot for an extended period of time.