This pattern is a bit formal and is mostly used in written Japanese or in formal speech. It connects two clauses, stating that something is true not just in the first way, but also in a second, often more surprising way. The second clause often contains words like も or まで to emphasize the addition.

It's similar to だけでなく, but ばかりか carries a nuance that the second point is notable or unexpected. For example, someone might be not only smart but also humble. Because it's formal, it's not common in casual conversation.

Note that the second clause often expresses something that goes beyond expectation, so it works well with verbs like 驚く or adjectives that are extreme. Also, the second clause is usually a full sentence, and the whole thing ends normally.