。
Her tone of voice was as if she were my mother.
Literal
[topic-は] just-as I [genitive-の] mother is-[as-if-such-as-かのような] speech-tone was.
口ぶり ('manner of speaking, tone') is concrete: the 'speech-look,' analogous to 顔つき for face. Pairs with similes via ~ような口ぶり ('a tone like X'). The full まるで~かのような construction with 私の母である ('be my mother') as the embedded simile gives 'a tone as if she were my mother' — implying she's speaking with the warmth, familiarity, or perhaps presumption of an actual mother, despite not being one. The context is left open: it could be approving (a comforting older friend) or critical (presumptuous, overstepping).