FIG. 1 is an isometric view of a combined toothbrush handle and irrigator appliance unit showing my new design;

FIG. 2 is front elevational view thereof, shown with the toothbrush head and the irrigator tip removed from their respective handles and placed in the stored position;

FIG. 3 is a rear elevational view thereof;

FIG. 4 is a top plan view thereof;

FIG. 5 is a left side elevational view thereof;

FIG. 6 is a right side elevational view thereof;

FIG. 7 is a front elevational view thereof but with a reservoir inverted to a storage position;

FIG. 8 is a rear elevational view thereof;

FIG. 9 is a top plan view thereof as in FIG. 7;

FIG. 10 is a left side elevational view thereof as in FIG. 7;

FIG. 11 is a right side elevational view thereof as in FIG. 7; and,

FIG. 12 is a bottom plan view thereof.

The broken lines showing of bristles are for illustrative purposes only and form no part of the claimed design.