  Accreting supermassive black holes (SMBHs) frequently power jets that
interact with the interstellar/circumgalactic medium (ISM/CGM), regulating
star-formation in the galaxy. Highly supersonic jets launched by active
galactic nuclei (AGN) power a cocoon that confines them and shocks the ambient
medium. We build upon the models of narrow conical jets interacting with a
smooth ambient medium, to include the effect of dense clouds that are an
essential ingredient of a multiphase ISM. The key physical ingredient of this
model is that the clouds along the supersonic jet-beam strongly decelerate the
jet-head, but the subsonic cocoon easily moves around the clouds without much
resistance. We propose scalings for important physical quantities -- cocoon
pressure, head & cocoon speed, and jet radius. We obtain, for the first time,
the analytic condition on clumpiness of the ambient medium for the jet to
dissipate within the cocoon and verify it with numerical simulations of conical
jets interacting with a uniform ISM with embedded spherical clouds. A jet is
defined to be dissipated when the cocoon speed exceeds the speed of the
jet-head. We compare our models to more sophisticated numerical simulations,
direct observations of jet-ISM interaction (e.g., quasar J1316+1753), and
discuss implications for the Fermi/eROSITA bubbles. Our work also motivates
effective subgrid models for AGN jet feedback in a clumpy ISM unresolved by the
present generation of cosmological galaxy formation simulations.
