Disclosed herein is a hair treatment composition containing a polymer selected from crosslinked copolymers of (meth)acrylic acid and (C1-C6)alkyl esters, cross-linked anionic acrylate polymers, and acrylic associative polymers; a carbomer compound; a fatty alcohol that is liquid at room temperature; a fatty substance other than the fatty alcohol that is liquid at room temperature; an anionic surfactant; an amphoteric surfactant; a basic compound; a cosmetically acceptable solvent; and optionally, a colorant compound. Also disclosed is a process for altering the color of hair involving applying onto hair, a composition comprising the hair treatment composition and an oxidizing composition.