She was both frank and obedient.

Literal

She [topic-は] frank was-also obedient was-also.

~でもあり~でもあった expresses dual qualities — 'was both X and Y.' でも marks each quality as additive. 率直 (そっちょく, 'frank') and 素直 (すなお, 'obedient, docile') are na-adjectives describing complementary personality traits.