Means 'not only ... but also ...'; it adds another (often stronger) point to what was said before.
彼は遅刻したばかりか、連絡もしてこなかった。
Not only was he late, but he also didn't even contact us.
その店は品揃えが悪いばかりか、値段も高い。
The store not only has a poor selection but also high prices.
彼女は美しいばかりか頭も良いので、羨ましい。
She's not only beautiful but also smart, which is enviable.