She is not only kind but also an honest person.

Literal

She [topic-は] kind [not only-ばかりではなく] honest person is.

The pattern ~ばかりではなく is a more emphatic variant of ~だけでなく, both meaning 'not only X but also Y.' ばかり ('nothing but, only') adds stronger emphasis to the base expectation before the contrasting addition. The ではなく is the negative of the copula ('it is not the case that it's only'), creating the 'not only' meaning.