FIG. 1 is an elevational side view of a mug with character-supporting handle cover showing my new and ornamental design, the opposite elevational side view being a mirror image,

FIG. 2 is a top plan view thereof,

FIG. 3 is a bottom plan view thereof,

FIG. 4 is a front elevational view thereof,

FIG. 5 is a rear elevational view thereof; and,

FIG. 6 is a partial cross section as seen along line 6—6 in FIG. 2.

The broken lines in FIGS. 1-6 are for illustrative purposes only and form no part of the claimed design.