〜ばかりか・〜ばかりでなく
not only … but (even)
Plain form / Noun + ばかりか … も / まで / さえ (な-adj + な)
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ばかりか adds something to a first point, usually something more surprising or more extreme: 彼は約束を忘れたばかりか、謝りもしなかった, "not only did he forget the promise, he didn't even apologise".
The second half often has も, まで or さえ to mark the addition: 大人ばかりか、子どもまで夢中になっている, "not only adults but even children are hooked".
It works for good things too: 安いばかりか、サービスもいい. ばかりでなく is a slightly more neutral equivalent, close to だけでなく.
Compare どころか, which rejects the first idea ("far from"). ばかりか keeps the first idea and piles more on top.
Examples
彼は約束を忘れたばかりか、謝りもしなかった。
Not only did he forget the promise, he didn't even apologise.
この店は安いばかりか、サービスもいい。
This shop is not only cheap, but its service is good too.
彼女は英語ばかりか、フランス語も話せる。
She speaks not only English but French as well.
雨が降ったばかりか、風も強かった。
Not only did it rain, but it was windy too.
大人ばかりか、子どもまで夢中になっている。
Not only adults but even children are hooked on it.